## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 1)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(-1.4)$$ and $$y(-1.4)$$ given the following system of IVPs.

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

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

$$x(-1.4)\approx -1.357$$ and $$y(-1.4)\approx -0.1167$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 2)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(-0.40)$$ and $$y(-0.40)$$ given the following system of IVPs.

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

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

$$x(-0.40)\approx -0.6627$$ and $$y(-0.40)\approx -1.231$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 3)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(2.3)$$ and $$y(2.3)$$ given the following system of IVPs.

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

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

$$x(2.3)\approx 1.283$$ and $$y(2.3)\approx -1.727$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 4)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

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

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

$$x(0.60)\approx 1.105$$ and $$y(0.60)\approx -0.5699$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 5)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

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

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

$$x(0.60)\approx 0.2463$$ and $$y(0.60)\approx 1.277$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 6)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(1.3)$$ and $$y(1.3)$$ given the following system of IVPs.

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

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

$$x(1.3)\approx 8.490$$ and $$y(1.3)\approx 4.582$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 7)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

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

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

$$x(0.30)\approx -1.154$$ and $$y(0.30)\approx -1.667$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 8)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(1.3)$$ and $$y(1.3)$$ given the following system of IVPs.

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

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

$$x(1.3)\approx -1.827$$ and $$y(1.3)\approx -3.460$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 9)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

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

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

$$x(0.30)\approx 0.1268$$ and $$y(0.30)\approx 3.912$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 10)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

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

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

$$x(0.60)\approx -1.751$$ and $$y(0.60)\approx 0.3600$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 11)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(2.3)$$ and $$y(2.3)$$ given the following system of IVPs.

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

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

$$x(2.3)\approx -0.7502$$ and $$y(2.3)\approx 0.2308$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 12)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(1.3)$$ and $$y(1.3)$$ given the following system of IVPs.

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

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

$$x(1.3)\approx -0.6836$$ and $$y(1.3)\approx 0.2074$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 13)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(-1.7)$$ and $$y(-1.7)$$ given the following system of IVPs.

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

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

$$x(-1.7)\approx -1.367$$ and $$y(-1.7)\approx -1.263$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 14)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

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

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

$$x(-0.70)\approx 5.716$$ and $$y(-0.70)\approx 0.08035$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 15)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

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

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

$$x(-0.70)\approx 1.110$$ and $$y(-0.70)\approx -6.628$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 16)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

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

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

$$x(-0.70)\approx 1.620$$ and $$y(-0.70)\approx 0.7901$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 17)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

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

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

$$x(-0.70)\approx -1.968$$ and $$y(-0.70)\approx 0.4260$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 18)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(-1.7)$$ and $$y(-1.7)$$ given the following system of IVPs.

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

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

$$x(-1.7)\approx 1.978$$ and $$y(-1.7)\approx -0.8414$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 19)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

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

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

$$x(0.30)\approx 0.2759$$ and $$y(0.30)\approx -1.106$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 20)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

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

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

$$x(0.30)\approx -1.555$$ and $$y(0.30)\approx 1.088$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 21)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(2.6)$$ and $$y(2.6)$$ given the following system of IVPs.

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

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

$$x(2.6)\approx 0.2049$$ and $$y(2.6)\approx -3.063$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 22)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

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

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

$$x(0.60)\approx 1.590$$ and $$y(0.60)\approx 2.007$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 23)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(1.3)$$ and $$y(1.3)$$ given the following system of IVPs.

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

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

$$x(1.3)\approx 13.13$$ and $$y(1.3)\approx -5.796$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 24)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(1.3)$$ and $$y(1.3)$$ given the following system of IVPs.

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

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

$$x(1.3)\approx -0.2153$$ and $$y(1.3)\approx -1.094$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 25)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

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

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

$$x(-0.70)\approx 4.729$$ and $$y(-0.70)\approx -4.399$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 26)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(-1.4)$$ and $$y(-1.4)$$ given the following system of IVPs.

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

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

$$x(-1.4)\approx -0.8088$$ and $$y(-1.4)\approx 0.6344$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 27)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(1.3)$$ and $$y(1.3)$$ given the following system of IVPs.

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

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

$$x(1.3)\approx -10.36$$ and $$y(1.3)\approx -13.47$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 28)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(-1.7)$$ and $$y(-1.7)$$ given the following system of IVPs.

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

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

$$x(-1.7)\approx 2.456$$ and $$y(-1.7)\approx -0.1348$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 29)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

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

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

$$x(0.30)\approx 0.04812$$ and $$y(0.30)\approx 3.033$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 30)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

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

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

$$x(-0.70)\approx 1.044$$ and $$y(-0.70)\approx -7.591$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 31)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

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

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

$$x(-0.70)\approx 0.7309$$ and $$y(-0.70)\approx -0.7151$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 32)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

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

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

$$x(0.60)\approx -1.475$$ and $$y(0.60)\approx 0.7611$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 33)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

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

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

$$x(0.60)\approx 2.949$$ and $$y(0.60)\approx 0.03386$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 34)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(1.3)$$ and $$y(1.3)$$ given the following system of IVPs.

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

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

$$x(1.3)\approx 4.159$$ and $$y(1.3)\approx -6.837$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 35)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(-0.40)$$ and $$y(-0.40)$$ given the following system of IVPs.

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

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

$$x(-0.40)\approx 0.2896$$ and $$y(-0.40)\approx 0.8183$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 36)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(-0.40)$$ and $$y(-0.40)$$ given the following system of IVPs.

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

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

$$x(-0.40)\approx 0.4277$$ and $$y(-0.40)\approx 1.001$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 37)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(2.3)$$ and $$y(2.3)$$ given the following system of IVPs.

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

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

$$x(2.3)\approx 24.13$$ and $$y(2.3)\approx 19.08$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 38)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(1.6)$$ and $$y(1.6)$$ given the following system of IVPs.

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

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

$$x(1.6)\approx -12.89$$ and $$y(1.6)\approx -3.994$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 39)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

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

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

$$x(0.60)\approx -4.541$$ and $$y(0.60)\approx 3.043$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 40)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(-1.7)$$ and $$y(-1.7)$$ given the following system of IVPs.

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

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

$$x(-1.7)\approx 0.3002$$ and $$y(-1.7)\approx 0.08715$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 41)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(1.3)$$ and $$y(1.3)$$ given the following system of IVPs.

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

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

$$x(1.3)\approx -0.2426$$ and $$y(1.3)\approx 0.5265$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 42)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

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

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

$$x(0.30)\approx -0.8581$$ and $$y(0.30)\approx -1.293$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 43)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(1.6)$$ and $$y(1.6)$$ given the following system of IVPs.

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

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

$$x(1.6)\approx -0.2420$$ and $$y(1.6)\approx -1.360$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 44)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(1.6)$$ and $$y(1.6)$$ given the following system of IVPs.

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

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

$$x(1.6)\approx -2.804$$ and $$y(1.6)\approx -2.313$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 45)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

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

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

$$x(-0.70)\approx 1.127$$ and $$y(-0.70)\approx 2.264$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 46)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(-0.70)$$ and $$y(-0.70)$$ given the following system of IVPs.

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

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

$$x(-0.70)\approx -0.01399$$ and $$y(-0.70)\approx -0.3053$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 47)

Use technology to implement Euler's method with $$h=0.020$$ to approximate $$x(0.60)$$ and $$y(0.60)$$ given the following system of IVPs.

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

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

$$x(0.60)\approx -0.7424$$ and $$y(0.60)\approx -1.150$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 48)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(2.3)$$ and $$y(2.3)$$ given the following system of IVPs.

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

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

$$x(2.3)\approx 0.2921$$ and $$y(2.3)\approx -0.3078$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 49)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

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

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

$$x(0.30)\approx -1.318$$ and $$y(0.30)\approx -0.08504$$.

## N3m - Programming Euler’s method. Implement Euler’s method using technology. (ver. 50)

Use technology to implement Euler's method with $$h=0.010$$ to approximate $$x(0.30)$$ and $$y(0.30)$$ given the following system of IVPs.

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

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

$$x(0.30)\approx 0.3189$$ and $$y(0.30)\approx 1.939$$.