## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 1)

Use Euler's method with $$h=0.20$$ to approximate $$x(-1.4)$$ and $$y(-1.4)$$ given the following system of IVPs.

$x'= -2 \, t y + 4 \, x y - 1\hspace{2em}x( -2 )= -2$

$y'= -2 \, x^{2} y + t y^{2} + 1\hspace{2em}y( -2 )= -2$

$$x(-1.8)\approx -0.6000$$ and $$y(-1.8)\approx -0.2000$$.

$$x(-1.6)\approx -0.8480$$ and $$y(-1.6)\approx 0.01440$$.

$$x(-1.4)\approx -1.049$$ and $$y(-1.4)\approx 0.2102$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 2)

Use Euler's method with $$h=0.20$$ to approximate $$x(-0.40)$$ and $$y(-0.40)$$ given the following system of IVPs.

$x'= -4 \, t^{2} x - t^{2} y - 3\hspace{2em}x( -1 )= 1$

$y'= t^{2} y^{2} + t x\hspace{2em}y( -1 )= -2$

$$x(-0.80)\approx 0.0000$$ and $$y(-0.80)\approx -1.400$$.

$$x(-0.60)\approx -0.4208$$ and $$y(-0.60)\approx -1.149$$.

$$x(-0.40)\approx -0.8169$$ and $$y(-0.40)\approx -1.004$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 3)

Use Euler's method with $$h=0.20$$ to approximate $$x(-1.4)$$ and $$y(-1.4)$$ given the following system of IVPs.

$x'= -4 \, t^{2} x^{2} + 4 \, t^{2} y - 1\hspace{2em}x( -2 )= 0$

$y'= -2 \, t^{2} x + 2 \, t y - 3\hspace{2em}y( -2 )= 0$

$$x(-1.8)\approx -0.2000$$ and $$y(-1.8)\approx -0.6000$$.

$$x(-1.6)\approx -2.059$$ and $$y(-1.6)\approx -0.5088$$.

$$x(-1.4)\approx -11.98$$ and $$y(-1.4)\approx 1.325$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 4)

Use Euler's method with $$h=0.20$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

$x'= -4 \, x^{2} y^{2} - 3 \, t x + 1\hspace{2em}x( 0 )= 2$

$y'= -t^{2} x - 2 \, t y - 1\hspace{2em}y( 0 )= 0$

$$x(0.20)\approx 2.200$$ and $$y(0.20)\approx -0.2000$$.

$$x(0.40)\approx 1.981$$ and $$y(0.40)\approx -0.4016$$.

$$x(0.60)\approx 1.199$$ and $$y(0.60)\approx -0.6007$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 5)

Use Euler's method with $$h=0.20$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

$x'= t x - 3 \, x y\hspace{2em}x( 0 )= 2$

$y'= t^{2} x - 4 \, t^{2} y + 1\hspace{2em}y( 0 )= 1$

$$x(0.20)\approx 0.8000$$ and $$y(0.20)\approx 1.200$$.

$$x(0.40)\approx 0.2560$$ and $$y(0.40)\approx 1.368$$.

$$x(0.60)\approx 0.06635$$ and $$y(0.60)\approx 1.401$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 6)

Use Euler's method with $$h=0.20$$ to approximate $$x(2.6)$$ and $$y(2.6)$$ given the following system of IVPs.

$x'= -4 \, t^{2} y^{2} + t x + 3\hspace{2em}x( 2 )= -2$

$y'= t^{2} x - 2 \, x y - 1\hspace{2em}y( 2 )= 2$

$$x(2.2)\approx -15.00$$ and $$y(2.2)\approx 1.800$$.

$$x(2.4)\approx -33.55$$ and $$y(2.4)\approx -2.120$$.

$$x(2.6)\approx -69.76$$ and $$y(2.6)\approx -69.41$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 7)

Use Euler's method with $$h=0.10$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

$x'= 4 \, t^{2} x^{2} + 3 \, t y\hspace{2em}x( 0 )= -1$

$y'= -4 \, t^{2} x + 2 \, t y^{2} - 3\hspace{2em}y( 0 )= -1$

$$x(0.10)\approx -1.000$$ and $$y(0.10)\approx -1.300$$.

$$x(0.20)\approx -1.035$$ and $$y(0.20)\approx -1.562$$.

$$x(0.30)\approx -1.112$$ and $$y(0.30)\approx -1.748$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 8)

Use Euler's method with $$h=0.10$$ to approximate $$x(1.3)$$ and $$y(1.3)$$ given the following system of IVPs.

$x'= 4 \, t^{2} x + 4 \, x y - 1\hspace{2em}x( 1 )= -2$

$y'= 2 \, t^{2} x + t y - 3\hspace{2em}y( 1 )= 0$

$$x(1.1)\approx -2.900$$ and $$y(1.1)\approx -0.7000$$.

$$x(1.2)\approx -3.592$$ and $$y(1.2)\approx -1.779$$.

$$x(1.3)\approx -3.205$$ and $$y(1.3)\approx -3.327$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 9)

Use Euler's method with $$h=0.10$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

$x'= -3 \, t^{2} x^{2} - x^{2} y^{2} - 1\hspace{2em}x( 0 )= 1$

$y'= 4 \, x^{2} y + 3 \, t y + 2\hspace{2em}y( 0 )= 2$

$$x(0.10)\approx 0.5000$$ and $$y(0.10)\approx 3.000$$.

$$x(0.20)\approx 0.1742$$ and $$y(0.20)\approx 3.590$$.

$$x(0.30)\approx 0.03475$$ and $$y(0.30)\approx 4.049$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 10)

Use Euler's method with $$h=0.20$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

$x'= -4 \, x^{2} y - 2 \, t y + 3\hspace{2em}x( 0 )= -2$

$y'= 3 \, t^{2} x + 4 \, t^{2} y + 1\hspace{2em}y( 0 )= 0$

$$x(0.20)\approx -1.400$$ and $$y(0.20)\approx 0.2000$$.

$$x(0.40)\approx -1.130$$ and $$y(0.40)\approx 0.3728$$.

$$x(0.60)\approx -0.9698$$ and $$y(0.60)\approx 0.5121$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 11)

Use Euler's method with $$h=0.20$$ to approximate $$x(-0.40)$$ and $$y(-0.40)$$ given the following system of IVPs.

$x'= -t y^{2} - 2 \, x y\hspace{2em}x( -1 )= 1$

$y'= 3 \, t^{2} y + 2 \, x^{2} y - 3\hspace{2em}y( -1 )= 0$

$$x(-0.80)\approx 1.000$$ and $$y(-0.80)\approx -0.6000$$.

$$x(-0.60)\approx 1.298$$ and $$y(-0.60)\approx -1.670$$.

$$x(-0.40)\approx 2.499$$ and $$y(-0.40)\approx -3.756$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 12)

Use Euler's method with $$h=0.10$$ to approximate $$x(1.3)$$ and $$y(1.3)$$ given the following system of IVPs.

$x'= 2 \, t^{2} y^{2} + 2 \, x^{2} y + 2\hspace{2em}x( 1 )= -2$

$y'= -4 \, x^{2} y^{2} + t x^{2} - 2\hspace{2em}y( 1 )= 1$

$$x(1.1)\approx -0.8000$$ and $$y(1.1)\approx -0.4000$$.

$$x(1.2)\approx -0.6125$$ and $$y(1.2)\approx -0.5706$$.

$$x(1.3)\approx -0.3615$$ and $$y(1.3)\approx -0.7744$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 13)

Use Euler's method with $$h=0.10$$ to approximate $$x(-1.7)$$ and $$y(-1.7)$$ given the following system of IVPs.

$x'= t^{2} y - x^{2} y + 3\hspace{2em}x( -2 )= -2$

$y'= x^{2} y^{2} + t y^{2}\hspace{2em}y( -2 )= -2$

$$x(-1.9)\approx -1.700$$ and $$y(-1.9)\approx -1.200$$.

$$x(-1.8)\approx -1.486$$ and $$y(-1.8)\approx -1.057$$.

$$x(-1.7)\approx -1.295$$ and $$y(-1.7)\approx -1.012$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 14)

Use Euler's method with $$h=0.10$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

$x'= 2 \, x^{2} y - 4 \, t y^{2} - 1\hspace{2em}x( -1 )= 2$

$y'= t x + 4 \, t y + 2\hspace{2em}y( -1 )= 1$

$$x(-0.90)\approx 3.100$$ and $$y(-0.90)\approx 0.6000$$.

$$x(-0.80)\approx 4.283$$ and $$y(-0.80)\approx 0.3050$$.

$$x(-0.70)\approx 5.331$$ and $$y(-0.70)\approx 0.06478$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 15)

Use Euler's method with $$h=0.10$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

$x'= 3 \, t x^{2} + t y - 1\hspace{2em}x( -1 )= 2$

$y'= -2 \, t x^{2} + 4 \, x^{2} y - 3\hspace{2em}y( -1 )= -1$

$$x(-0.90)\approx 0.8000$$ and $$y(-0.90)\approx -2.100$$.

$$x(-0.80)\approx 0.7162$$ and $$y(-0.80)\approx -2.822$$.

$$x(-0.70)\approx 0.7189$$ and $$y(-0.70)\approx -3.619$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 16)

Use Euler's method with $$h=0.10$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

$x'= x^{2} y^{2} + t y + 2\hspace{2em}x( -1 )= 1$

$y'= 2 \, t^{2} y^{2} + 2 \, x y^{2} + 2\hspace{2em}y( -1 )= 0$

$$x(-0.90)\approx 1.200$$ and $$y(-0.90)\approx 0.2000$$.

$$x(-0.80)\approx 1.388$$ and $$y(-0.80)\approx 0.4161$$.

$$x(-0.70)\approx 1.588$$ and $$y(-0.70)\approx 0.6863$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 17)

Use Euler's method with $$h=0.10$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

$x'= 2 \, x^{2} y + 2 \, t y^{2} - 2\hspace{2em}x( -1 )= -2$

$y'= t^{2} y^{2} + 3 \, x y + 3\hspace{2em}y( -1 )= 0$

$$x(-0.90)\approx -2.200$$ and $$y(-0.90)\approx 0.3000$$.

$$x(-0.80)\approx -2.126$$ and $$y(-0.80)\approx 0.4093$$.

$$x(-0.70)\approx -1.983$$ and $$y(-0.70)\approx 0.4590$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 18)

Use Euler's method with $$h=0.10$$ to approximate $$x(-1.7)$$ and $$y(-1.7)$$ given the following system of IVPs.

$x'= -3 \, t^{2} y - 4 \, t x\hspace{2em}x( -2 )= 0$

$y'= 2 \, t x^{2} - 4 \, x y - 2\hspace{2em}y( -2 )= 0$

$$x(-1.9)\approx 0.0000$$ and $$y(-1.9)\approx -0.2000$$.

$$x(-1.8)\approx 0.2166$$ and $$y(-1.8)\approx -0.4000$$.

$$x(-1.7)\approx 0.7614$$ and $$y(-1.7)\approx -0.5822$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 19)

Use Euler's method with $$h=0.10$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

$x'= -2 \, x^{2} y^{2} + 2 \, t x - 3\hspace{2em}x( 0 )= 2$

$y'= 3 \, t^{2} y^{2} - x^{2} y^{2} + 1\hspace{2em}y( 0 )= -1$

$$x(0.10)\approx 0.9000$$ and $$y(0.10)\approx -1.300$$.

$$x(0.20)\approx 0.3442$$ and $$y(0.20)\approx -1.332$$.

$$x(0.30)\approx 0.01596$$ and $$y(0.30)\approx -1.232$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 20)

Use Euler's method with $$h=0.10$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

$x'= 3 \, t^{2} y^{2} - 4 \, x^{2} y^{2} - 3\hspace{2em}x( 0 )= 0$

$y'= -t^{2} y + x y^{2} + 1\hspace{2em}y( 0 )= 1$

$$x(0.10)\approx -0.3000$$ and $$y(0.10)\approx 1.100$$.

$$x(0.20)\approx -0.6399$$ and $$y(0.20)\approx 1.163$$.

$$x(0.30)\approx -1.145$$ and $$y(0.30)\approx 1.171$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 21)

Use Euler's method with $$h=0.20$$ to approximate $$x(1.6)$$ and $$y(1.6)$$ given the following system of IVPs.

$x'= -2 \, t x^{2} + x^{2} y\hspace{2em}x( 1 )= 2$

$y'= 2 \, t^{2} x^{2} + 2 \, t^{2} y - 2\hspace{2em}y( 1 )= 0$

$$x(1.2)\approx 0.4000$$ and $$y(1.2)\approx 1.200$$.

$$x(1.4)\approx 0.3616$$ and $$y(1.4)\approx 1.583$$.

$$x(1.6)\approx 0.3298$$ and $$y(1.6)\approx 2.527$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 22)

Use Euler's method with $$h=0.20$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

$x'= -x^{2} y + 4 \, t x + 3\hspace{2em}x( 0 )= 0$

$y'= -2 \, t^{2} y^{2} + 3 \, t^{2} x + 2\hspace{2em}y( 0 )= 1$

$$x(0.20)\approx 0.6000$$ and $$y(0.20)\approx 1.400$$.

$$x(0.40)\approx 1.195$$ and $$y(0.40)\approx 1.783$$.

$$x(0.60)\approx 1.668$$ and $$y(0.60)\approx 2.094$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 23)

Use Euler's method with $$h=0.10$$ to approximate $$x(1.3)$$ and $$y(1.3)$$ given the following system of IVPs.

$x'= -t x^{2} - 4 \, x y + 3\hspace{2em}x( 1 )= 2$

$y'= -3 \, t x - 3 \, t y - 3\hspace{2em}y( 1 )= -2$

$$x(1.1)\approx 3.500$$ and $$y(1.1)\approx -2.300$$.

$$x(1.2)\approx 5.672$$ and $$y(1.2)\approx -2.996$$.

$$x(1.3)\approx 8.909$$ and $$y(1.3)\approx -4.260$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 24)

Use Euler's method with $$h=0.10$$ to approximate $$x(1.3)$$ and $$y(1.3)$$ given the following system of IVPs.

$x'= 2 \, t^{2} y^{2} - 4 \, x^{2} y^{2} + 2\hspace{2em}x( 1 )= -1$

$y'= -3 \, x^{2} y + 2 \, t y - 3\hspace{2em}y( 1 )= 0$

$$x(1.1)\approx -0.8000$$ and $$y(1.1)\approx -0.3000$$.

$$x(1.2)\approx -0.6013$$ and $$y(1.2)\approx -0.6084$$.

$$x(1.3)\approx -0.3482$$ and $$y(1.3)\approx -0.9884$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 25)

Use Euler's method with $$h=0.10$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

$x'= 2 \, x y^{2} + 4 \, t y - 1\hspace{2em}x( -1 )= 2$

$y'= 2 \, t x^{2} - 2 \, x y^{2} - 3\hspace{2em}y( -1 )= 2$

$$x(-0.90)\approx 2.700$$ and $$y(-0.90)\approx -0.7000$$.

$$x(-0.80)\approx 3.117$$ and $$y(-0.80)\approx -2.577$$.

$$x(-0.70)\approx 7.980$$ and $$y(-0.70)\approx -8.570$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 26)

Use Euler's method with $$h=0.20$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

$x'= t^{2} y^{2} - x y - 3\hspace{2em}x( 0 )= 0$

$y'= -4 \, x^{2} y^{2} - 4 \, t x + 2\hspace{2em}y( 0 )= 1$

$$x(0.20)\approx -0.6000$$ and $$y(0.20)\approx 1.400$$.

$$x(0.40)\approx -1.016$$ and $$y(0.40)\approx 1.332$$.

$$x(0.60)\approx -1.289$$ and $$y(0.60)\approx 0.5917$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 27)

Use Euler's method with $$h=0.10$$ to approximate $$x(1.3)$$ and $$y(1.3)$$ given the following system of IVPs.

$x'= x y^{2} - 4 \, t y + 1\hspace{2em}x( 1 )= -2$

$y'= -3 \, t^{2} x^{2} - 4 \, x y + 2\hspace{2em}y( 1 )= 0$

$$x(1.1)\approx -1.900$$ and $$y(1.1)\approx -1.000$$.

$$x(1.2)\approx -1.550$$ and $$y(1.2)\approx -2.870$$.

$$x(1.3)\approx -1.349$$ and $$y(1.3)\approx -5.488$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 28)

Use Euler's method with $$h=0.10$$ to approximate $$x(-1.7)$$ and $$y(-1.7)$$ given the following system of IVPs.

$x'= 2 \, t^{2} x - 4 \, t y^{2}\hspace{2em}x( -2 )= 0$

$y'= -4 \, x^{2} y + 2 \, t y - 3\hspace{2em}y( -2 )= 1$

$$x(-1.9)\approx 0.8000$$ and $$y(-1.9)\approx 0.3000$$.

$$x(-1.8)\approx 1.446$$ and $$y(-1.8)\approx -0.1908$$.

$$x(-1.7)\approx 2.409$$ and $$y(-1.7)\approx -0.2625$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 29)

Use Euler's method with $$h=0.10$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

$x'= -4 \, t^{2} y^{2} - x y^{2}\hspace{2em}x( 0 )= 2$

$y'= 4 \, t^{2} y^{2} + 2 \, x y - 2\hspace{2em}y( 0 )= 2$

$$x(0.10)\approx 1.200$$ and $$y(0.10)\approx 2.600$$.

$$x(0.20)\approx 0.3618$$ and $$y(0.20)\approx 3.051$$.

$$x(0.30)\approx -0.1239$$ and $$y(0.30)\approx 3.221$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 30)

Use Euler's method with $$h=0.10$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

$x'= 2 \, t x^{2} + t y - 2\hspace{2em}x( -1 )= 1$

$y'= 4 \, t x - 4 \, t y - 1\hspace{2em}y( -1 )= -2$

$$x(-0.90)\approx 0.8000$$ and $$y(-0.90)\approx -3.300$$.

$$x(-0.80)\approx 0.7818$$ and $$y(-0.80)\approx -4.876$$.

$$x(-0.70)\approx 0.8741$$ and $$y(-0.70)\approx -6.786$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 31)

Use Euler's method with $$h=0.10$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

$x'= -4 \, x^{2} y^{2} + t x + 3\hspace{2em}x( -1 )= 0$

$y'= 2 \, x^{2} y^{2} - 2 \, t^{2} y - 3\hspace{2em}y( -1 )= 0$

$$x(-0.90)\approx 0.3000$$ and $$y(-0.90)\approx -0.3000$$.

$$x(-0.80)\approx 0.5698$$ and $$y(-0.80)\approx -0.5498$$.

$$x(-0.70)\approx 0.7849$$ and $$y(-0.70)\approx -0.7598$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 32)

Use Euler's method with $$h=0.20$$ to approximate $$x(-1.4)$$ and $$y(-1.4)$$ given the following system of IVPs.

$x'= 3 \, t^{2} x + 2 \, x y + 1\hspace{2em}x( -2 )= -2$

$y'= -2 \, t y^{2} + 2 \, x y - 3\hspace{2em}y( -2 )= -1$

$$x(-1.8)\approx -5.800$$ and $$y(-1.8)\approx 0.0000$$.

$$x(-1.6)\approx -16.88$$ and $$y(-1.6)\approx -0.6000$$.

$$x(-1.4)\approx -38.55$$ and $$y(-1.4)\approx 3.080$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 33)

Use Euler's method with $$h=0.10$$ to approximate $$x(-1.7)$$ and $$y(-1.7)$$ given the following system of IVPs.

$x'= -t^{2} x^{2} + x y^{2} + 2\hspace{2em}x( -2 )= -2$

$y'= -4 \, t^{2} y^{2} + t^{2} x + 2\hspace{2em}y( -2 )= 1$

$$x(-1.9)\approx -3.600$$ and $$y(-1.9)\approx -1.200$$.

$$x(-1.8)\approx -8.597$$ and $$y(-1.8)\approx -4.379$$.

$$x(-1.7)\approx -48.83$$ and $$y(-1.7)\approx -31.82$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 34)

Use Euler's method with $$h=0.10$$ to approximate $$x(-1.7)$$ and $$y(-1.7)$$ given the following system of IVPs.

$x'= 3 \, t^{2} x^{2} + 4 \, x y - 3\hspace{2em}x( -2 )= 1$

$y'= -t y - 2 \, x y + 1\hspace{2em}y( -2 )= -1$

$$x(-1.9)\approx 1.500$$ and $$y(-1.9)\approx -0.9000$$.

$$x(-1.8)\approx 3.097$$ and $$y(-1.8)\approx -0.7010$$.

$$x(-1.7)\approx 11.25$$ and $$y(-1.7)\approx -0.2930$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 35)

Use Euler's method with $$h=0.20$$ to approximate $$x(-0.40)$$ and $$y(-0.40)$$ given the following system of IVPs.

$x'= 2 \, t^{2} x^{2} + 3 \, t^{2} y - 1\hspace{2em}x( -1 )= 0$

$y'= -4 \, x^{2} y^{2} + 2 \, t y^{2} + 1\hspace{2em}y( -1 )= 1$

$$x(-0.80)\approx 0.4000$$ and $$y(-0.80)\approx 0.8000$$.

$$x(-0.60)\approx 0.5482$$ and $$y(-0.60)\approx 0.7133$$.

$$x(-0.40)\approx 0.5455$$ and $$y(-0.40)\approx 0.6689$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 36)

Use Euler's method with $$h=0.20$$ to approximate $$x(-0.40)$$ and $$y(-0.40)$$ given the following system of IVPs.

$x'= -2 \, x^{2} y^{2} - 4 \, t^{2} x\hspace{2em}x( -1 )= 2$

$y'= 3 \, x y^{2} + 3 \, t y + 2\hspace{2em}y( -1 )= 0$

$$x(-0.80)\approx 0.4000$$ and $$y(-0.80)\approx 0.4000$$.

$$x(-0.60)\approx 0.1850$$ and $$y(-0.60)\approx 0.6464$$.

$$x(-0.40)\approx 0.1260$$ and $$y(-0.40)\approx 0.8601$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 37)

Use Euler's method with $$h=0.10$$ to approximate $$x(2.3)$$ and $$y(2.3)$$ given the following system of IVPs.

$x'= -t^{2} x^{2} + 4 \, t y^{2} - 1\hspace{2em}x( 2 )= 2$

$y'= 4 \, t^{2} x - 3 \, t^{2} y\hspace{2em}y( 2 )= 2$

$$x(2.1)\approx 3.500$$ and $$y(2.1)\approx 2.800$$.

$$x(2.2)\approx 4.583$$ and $$y(2.2)\approx 5.270$$.

$$x(2.3)\approx 18.75$$ and $$y(2.3)\approx 6.492$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 38)

Use Euler's method with $$h=0.20$$ to approximate $$x(1.6)$$ and $$y(1.6)$$ given the following system of IVPs.

$x'= -t^{2} x^{2} + 3 \, t^{2} y + 1\hspace{2em}x( 1 )= 0$

$y'= x^{2} y + t y^{2} + 3\hspace{2em}y( 1 )= -2$

$$x(1.2)\approx -1.000$$ and $$y(1.2)\approx -0.6000$$.

$$x(1.4)\approx -1.606$$ and $$y(1.4)\approx -0.03360$$.

$$x(1.6)\approx -2.457$$ and $$y(1.6)\approx 0.5494$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 39)

Use Euler's method with $$h=0.20$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

$x'= -3 \, t y^{2} - 4 \, t x - 2\hspace{2em}x( 0 )= -1$

$y'= -2 \, t^{2} y^{2} - 2 \, t^{2} x + 3\hspace{2em}y( 0 )= 2$

$$x(0.20)\approx -1.400$$ and $$y(0.20)\approx 2.600$$.

$$x(0.40)\approx -2.387$$ and $$y(0.40)\approx 3.114$$.

$$x(0.60)\approx -4.351$$ and $$y(0.60)\approx 3.246$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 40)

Use Euler's method with $$h=0.10$$ to approximate $$x(-1.7)$$ and $$y(-1.7)$$ given the following system of IVPs.

$x'= -t^{2} y^{2} + 3 \, x^{2} y + 1\hspace{2em}x( -2 )= 0$

$y'= 3 \, t^{2} x^{2} + 4 \, x y\hspace{2em}y( -2 )= 0$

$$x(-1.9)\approx 0.1000$$ and $$y(-1.9)\approx 0.0000$$.

$$x(-1.8)\approx 0.2000$$ and $$y(-1.8)\approx 0.01083$$.

$$x(-1.7)\approx 0.3001$$ and $$y(-1.7)\approx 0.05058$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 41)

Use Euler's method with $$h=0.10$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

$x'= 2 \, t^{2} x^{2} - 4 \, t^{2} y\hspace{2em}x( -1 )= 1$

$y'= t x^{2} - x y^{2} - 3\hspace{2em}y( -1 )= -2$

$$x(-0.90)\approx 2.000$$ and $$y(-0.90)\approx -2.800$$.

$$x(-0.80)\approx 3.555$$ and $$y(-0.80)\approx -5.028$$.

$$x(-0.70)\approx 6.460$$ and $$y(-0.70)\approx -15.33$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 42)

Use Euler's method with $$h=0.10$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

$x'= 4 \, t^{2} y^{2} - 2 \, x y^{2}\hspace{2em}x( 0 )= -2$

$y'= -t^{2} y^{2} - 2 \, t^{2} x - 1\hspace{2em}y( 0 )= -1$

$$x(0.10)\approx -1.600$$ and $$y(0.10)\approx -1.100$$.

$$x(0.20)\approx -1.208$$ and $$y(0.20)\approx -1.198$$.

$$x(0.30)\approx -0.8383$$ and $$y(0.30)\approx -1.294$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 43)

Use Euler's method with $$h=0.20$$ to approximate $$x(2.6)$$ and $$y(2.6)$$ given the following system of IVPs.

$x'= t^{2} x + 2 \, t y + 3\hspace{2em}x( 2 )= -2$

$y'= -3 \, x^{2} y + 4 \, t y + 3\hspace{2em}y( 2 )= 2$

$$x(2.2)\approx -1.400$$ and $$y(2.2)\approx 1.000$$.

$$x(2.4)\approx -1.275$$ and $$y(2.4)\approx 2.184$$.

$$x(2.6)\approx -0.04759$$ and $$y(2.6)\approx 4.846$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 44)

Use Euler's method with $$h=0.20$$ to approximate $$x(1.6)$$ and $$y(1.6)$$ given the following system of IVPs.

$x'= -t^{2} y^{2} - t x - 3\hspace{2em}x( 1 )= -1$

$y'= 4 \, t^{2} x - 4 \, t y + 3\hspace{2em}y( 1 )= 1$

$$x(1.2)\approx -1.600$$ and $$y(1.2)\approx 0.0000$$.

$$x(1.4)\approx -1.816$$ and $$y(1.4)\approx -1.243$$.

$$x(1.6)\approx -2.513$$ and $$y(1.6)\approx -2.098$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 45)

Use Euler's method with $$h=0.10$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

$x'= -x^{2} y + t y + 2\hspace{2em}x( -1 )= 2$

$y'= x^{2} y^{2} - 3 \, t^{2} y + 2\hspace{2em}y( -1 )= 1$

$$x(-0.90)\approx 1.700$$ and $$y(-0.90)\approx 1.300$$.

$$x(-0.80)\approx 1.407$$ and $$y(-0.80)\approx 1.673$$.

$$x(-0.70)\approx 1.142$$ and $$y(-0.70)\approx 2.105$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 46)

Use Euler's method with $$h=0.10$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

$x'= -2 \, t^{2} y^{2} - 4 \, x^{2} y + 3\hspace{2em}x( -1 )= -1$

$y'= 4 \, t^{2} x^{2} + 2 \, t y^{2} + 2\hspace{2em}y( -1 )= -1$

$$x(-0.90)\approx -0.5000$$ and $$y(-0.90)\approx -0.6000$$.

$$x(-0.80)\approx -0.1983$$ and $$y(-0.80)\approx -0.3838$$.

$$x(-0.70)\approx 0.08886$$ and $$y(-0.70)\approx -0.1973$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 47)

Use Euler's method with $$h=0.20$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

$x'= -x^{2} y - t y^{2} - 3\hspace{2em}x( 0 )= 1$

$y'= 4 \, x^{2} y^{2} + 2 \, t x - 1\hspace{2em}y( 0 )= -2$

$$x(0.20)\approx 0.8000$$ and $$y(0.20)\approx 1.000$$.

$$x(0.40)\approx 0.03200$$ and $$y(0.40)\approx 1.376$$.

$$x(0.60)\approx -0.7197$$ and $$y(0.60)\approx 1.183$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 48)

Use Euler's method with $$h=0.10$$ to approximate $$x(2.3)$$ and $$y(2.3)$$ given the following system of IVPs.

$x'= 3 \, x^{2} y + 3 \, t y^{2} + 3\hspace{2em}x( 2 )= -1$

$y'= t^{2} x^{2} + t^{2} y^{2}\hspace{2em}y( 2 )= -1$

$$x(2.1)\approx -0.4000$$ and $$y(2.1)\approx -0.2000$$.

$$x(2.2)\approx -0.08440$$ and $$y(2.2)\approx -0.1118$$.

$$x(2.3)\approx 0.2236$$ and $$y(2.3)\approx -0.1023$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 49)

Use Euler's method with $$h=0.10$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

$x'= 4 \, t x^{2} + 2 \, t^{2} y - 2\hspace{2em}x( 0 )= -1$

$y'= -4 \, t^{2} y^{2} + 2 \, x y^{2} - 3\hspace{2em}y( 0 )= 1$

$$x(0.10)\approx -1.200$$ and $$y(0.10)\approx 0.5000$$.

$$x(0.20)\approx -1.341$$ and $$y(0.20)\approx 0.1390$$.

$$x(0.30)\approx -1.396$$ and $$y(0.30)\approx -0.1665$$.

## N2 - Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method. (ver. 50)

Use Euler's method with $$h=0.10$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

$x'= -3 \, t^{2} x^{2} - 2 \, x^{2} y^{2}\hspace{2em}x( 0 )= 1$

$y'= -2 \, x^{2} y^{2} + t^{2} y + 2\hspace{2em}y( 0 )= 2$

$$x(0.10)\approx 0.2000$$ and $$y(0.10)\approx 1.400$$.

$$x(0.20)\approx 0.1842$$ and $$y(0.20)\approx 1.586$$.

$$x(0.30)\approx 0.1667$$ and $$y(0.30)\approx 1.775$$.