## C2 - Non-homogeneous first-order linear ODE (ver. 1)

Find the general solution to the given ODE.

${y'} - 5 \, {y} = -9 \, \cos\left(-3 \, t\right) e^{\left(5 \, t\right)}$

$y= k e^{\left(5 \, t\right)} + 3 \, e^{\left(5 \, t\right)} \sin\left(-3 \, t\right)$

## C2 - Non-homogeneous first-order linear ODE (ver. 2)

Find the general solution to the given ODE.

${y'} + 5 \, {y} = 2 \, \cos\left(-t\right) e^{\left(-5 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} - 2 \, e^{\left(-5 \, t\right)} \sin\left(-t\right)$

## C2 - Non-homogeneous first-order linear ODE (ver. 3)

Find the general solution to the given ODE.

${y'} - 3 \, {y} = 15 \, e^{\left(3 \, t\right)} \sin\left(-5 \, t\right)$

$y= k e^{\left(3 \, t\right)} + 3 \, \cos\left(-5 \, t\right) e^{\left(3 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 4)

Find the general solution to the given ODE.

${y'} + 4 \, {y} = 15 \, e^{t}$

$y= k e^{\left(-4 \, t\right)} + 3 \, e^{t}$

## C2 - Non-homogeneous first-order linear ODE (ver. 5)

Find the general solution to the given ODE.

${y'} - {y} = 2 \, e^{t}$

$y= k e^{t} + 2 \, t e^{t}$

## C2 - Non-homogeneous first-order linear ODE (ver. 6)

Find the general solution to the given ODE.

${y'} - 5 \, {y} = 2 \, e^{\left(5 \, t\right)}$

$y= k e^{\left(5 \, t\right)} + 2 \, t e^{\left(5 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 7)

Find the general solution to the given ODE.

${y'} - 5 \, {y} = 9 \, \cos\left(3 \, t\right) e^{\left(5 \, t\right)}$

$y= k e^{\left(5 \, t\right)} + 3 \, e^{\left(5 \, t\right)} \sin\left(3 \, t\right)$

## C2 - Non-homogeneous first-order linear ODE (ver. 8)

Find the general solution to the given ODE.

${y'} - 5 \, {y} = 9 \, e^{\left(5 \, t\right)} \sin\left(-3 \, t\right)$

$y= k e^{\left(5 \, t\right)} + 3 \, \cos\left(-3 \, t\right) e^{\left(5 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 9)

Find the general solution to the given ODE.

${y'} + 4 \, {y} = -3 \, e^{\left(-4 \, t\right)}$

$y= k e^{\left(-4 \, t\right)} - 3 \, t e^{\left(-4 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 10)

Find the general solution to the given ODE.

${y'} + 5 \, {y} = 6 \, e^{\left(-3 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} + 3 \, e^{\left(-3 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 11)

Find the general solution to the given ODE.

${y'} + 3 \, {y} = -4 \, e^{\left(-t\right)}$

$y= k e^{\left(-3 \, t\right)} - 2 \, e^{\left(-t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 12)

Find the general solution to the given ODE.

${y'} - 3 \, {y} = -4 \, e^{\left(3 \, t\right)} \sin\left(2 \, t\right)$

$y= k e^{\left(3 \, t\right)} + 2 \, \cos\left(2 \, t\right) e^{\left(3 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 13)

Find the general solution to the given ODE.

${y'} - 2 \, {y} = -3 \, e^{\left(2 \, t\right)}$

$y= k e^{\left(2 \, t\right)} - 3 \, t e^{\left(2 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 14)

Find the general solution to the given ODE.

${y'} + {y} = 10 \, \cos\left(-5 \, t\right) e^{\left(-t\right)}$

$y= k e^{\left(-t\right)} - 2 \, e^{\left(-t\right)} \sin\left(-5 \, t\right)$

## C2 - Non-homogeneous first-order linear ODE (ver. 15)

Find the general solution to the given ODE.

${y'} - 4 \, {y} = -6 \, e^{t}$

$y= k e^{\left(4 \, t\right)} + 2 \, e^{t}$

## C2 - Non-homogeneous first-order linear ODE (ver. 16)

Find the general solution to the given ODE.

${y'} - 3 \, {y} = 3 \, e^{\left(3 \, t\right)} \sin\left(t\right)$

$y= k e^{\left(3 \, t\right)} - 3 \, \cos\left(t\right) e^{\left(3 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 17)

Find the general solution to the given ODE.

${y'} + 3 \, {y} = -6 \, \cos\left(3 \, t\right) e^{\left(-3 \, t\right)}$

$y= k e^{\left(-3 \, t\right)} - 2 \, e^{\left(-3 \, t\right)} \sin\left(3 \, t\right)$

## C2 - Non-homogeneous first-order linear ODE (ver. 18)

Find the general solution to the given ODE.

${y'} + 5 \, {y} = 3 \, e^{\left(-5 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} + 3 \, t e^{\left(-5 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 19)

Find the general solution to the given ODE.

${y'} - 2 \, {y} = -2 \, e^{\left(2 \, t\right)}$

$y= k e^{\left(2 \, t\right)} - 2 \, t e^{\left(2 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 20)

Find the general solution to the given ODE.

${y'} - 3 \, {y} = -15 \, e^{\left(3 \, t\right)} \sin\left(-5 \, t\right)$

$y= k e^{\left(3 \, t\right)} - 3 \, \cos\left(-5 \, t\right) e^{\left(3 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 21)

Find the general solution to the given ODE.

${y'} + 2 \, {y} = 3 \, e^{\left(-2 \, t\right)}$

$y= k e^{\left(-2 \, t\right)} + 3 \, t e^{\left(-2 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 22)

Find the general solution to the given ODE.

${y'} + 2 \, {y} = 3 \, e^{\left(-2 \, t\right)} \sin\left(-t\right)$

$y= k e^{\left(-2 \, t\right)} + 3 \, \cos\left(-t\right) e^{\left(-2 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 23)

Find the general solution to the given ODE.

${y'} + {y} = -8 \, e^{\left(-5 \, t\right)}$

$y= k e^{\left(-t\right)} + 2 \, e^{\left(-5 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 24)

Find the general solution to the given ODE.

${y'} - 3 \, {y} = 3 \, e^{\left(3 \, t\right)}$

$y= k e^{\left(3 \, t\right)} + 3 \, t e^{\left(3 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 25)

Find the general solution to the given ODE.

${y'} - 3 \, {y} = 10 \, e^{\left(3 \, t\right)} \sin\left(5 \, t\right)$

$y= k e^{\left(3 \, t\right)} - 2 \, \cos\left(5 \, t\right) e^{\left(3 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 26)

Find the general solution to the given ODE.

${y'} - 5 \, {y} = -2 \, e^{\left(5 \, t\right)} \sin\left(t\right)$

$y= k e^{\left(5 \, t\right)} + 2 \, \cos\left(t\right) e^{\left(5 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 27)

Find the general solution to the given ODE.

${y'} - {y} = 15 \, \cos\left(-5 \, t\right) e^{t}$

$y= k e^{t} - 3 \, e^{t} \sin\left(-5 \, t\right)$

## C2 - Non-homogeneous first-order linear ODE (ver. 28)

Find the general solution to the given ODE.

${y'} - 3 \, {y} = -15 \, e^{\left(3 \, t\right)} \sin\left(-5 \, t\right)$

$y= k e^{\left(3 \, t\right)} - 3 \, \cos\left(-5 \, t\right) e^{\left(3 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 29)

Find the general solution to the given ODE.

${y'} - 5 \, {y} = -4 \, \cos\left(-2 \, t\right) e^{\left(5 \, t\right)}$

$y= k e^{\left(5 \, t\right)} + 2 \, e^{\left(5 \, t\right)} \sin\left(-2 \, t\right)$

## C2 - Non-homogeneous first-order linear ODE (ver. 30)

Find the general solution to the given ODE.

${y'} - 2 \, {y} = -2 \, e^{t}$

$y= k e^{\left(2 \, t\right)} + 2 \, e^{t}$

## C2 - Non-homogeneous first-order linear ODE (ver. 31)

Find the general solution to the given ODE.

${y'} - {y} = 3 \, e^{t}$

$y= k e^{t} + 3 \, t e^{t}$

## C2 - Non-homogeneous first-order linear ODE (ver. 32)

Find the general solution to the given ODE.

${y'} - 3 \, {y} = 8 \, e^{\left(3 \, t\right)} \sin\left(4 \, t\right)$

$y= k e^{\left(3 \, t\right)} - 2 \, \cos\left(4 \, t\right) e^{\left(3 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 33)

Find the general solution to the given ODE.

${y'} + {y} = -15 \, \cos\left(5 \, t\right) e^{\left(-t\right)}$

$y= k e^{\left(-t\right)} - 3 \, e^{\left(-t\right)} \sin\left(5 \, t\right)$

## C2 - Non-homogeneous first-order linear ODE (ver. 34)

Find the general solution to the given ODE.

${y'} - 4 \, {y} = 6 \, e^{\left(4 \, t\right)} \sin\left(-2 \, t\right)$

$y= k e^{\left(4 \, t\right)} + 3 \, \cos\left(-2 \, t\right) e^{\left(4 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 35)

Find the general solution to the given ODE.

${y'} - 2 \, {y} = -6 \, e^{\left(2 \, t\right)} \sin\left(3 \, t\right)$

$y= k e^{\left(2 \, t\right)} + 2 \, \cos\left(3 \, t\right) e^{\left(2 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 36)

Find the general solution to the given ODE.

${y'} + 5 \, {y} = -4 \, e^{\left(-3 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} - 2 \, e^{\left(-3 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 37)

Find the general solution to the given ODE.

${y'} - 4 \, {y} = 10 \, \cos\left(-5 \, t\right) e^{\left(4 \, t\right)}$

$y= k e^{\left(4 \, t\right)} - 2 \, e^{\left(4 \, t\right)} \sin\left(-5 \, t\right)$

## C2 - Non-homogeneous first-order linear ODE (ver. 38)

Find the general solution to the given ODE.

${y'} + 2 \, {y} = 3 \, e^{\left(-2 \, t\right)} \sin\left(t\right)$

$y= k e^{\left(-2 \, t\right)} - 3 \, \cos\left(t\right) e^{\left(-2 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 39)

Find the general solution to the given ODE.

${y'} + 5 \, {y} = -3 \, e^{\left(-4 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} - 3 \, e^{\left(-4 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 40)

Find the general solution to the given ODE.

${y'} + 2 \, {y} = -2 \, \cos\left(-t\right) e^{\left(-2 \, t\right)}$

$y= k e^{\left(-2 \, t\right)} + 2 \, e^{\left(-2 \, t\right)} \sin\left(-t\right)$

## C2 - Non-homogeneous first-order linear ODE (ver. 41)

Find the general solution to the given ODE.

${y'} - 2 \, {y} = -10 \, e^{\left(2 \, t\right)} \sin\left(-5 \, t\right)$

$y= k e^{\left(2 \, t\right)} - 2 \, \cos\left(-5 \, t\right) e^{\left(2 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 42)

Find the general solution to the given ODE.

${y'} - 2 \, {y} = -2 \, e^{\left(2 \, t\right)}$

$y= k e^{\left(2 \, t\right)} - 2 \, t e^{\left(2 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 43)

Find the general solution to the given ODE.

${y'} - 2 \, {y} = -6 \, e^{\left(2 \, t\right)} \sin\left(3 \, t\right)$

$y= k e^{\left(2 \, t\right)} + 2 \, \cos\left(3 \, t\right) e^{\left(2 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 44)

Find the general solution to the given ODE.

${y'} + {y} = -6 \, e^{\left(-3 \, t\right)}$

$y= k e^{\left(-t\right)} + 3 \, e^{\left(-3 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 45)

Find the general solution to the given ODE.

${y'} - 5 \, {y} = -3 \, e^{\left(5 \, t\right)}$

$y= k e^{\left(5 \, t\right)} - 3 \, t e^{\left(5 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 46)

Find the general solution to the given ODE.

${y'} - 2 \, {y} = -15 \, e^{\left(-3 \, t\right)}$

$y= k e^{\left(2 \, t\right)} + 3 \, e^{\left(-3 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 47)

Find the general solution to the given ODE.

${y'} + 5 \, {y} = -3 \, e^{\left(-5 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} - 3 \, t e^{\left(-5 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 48)

Find the general solution to the given ODE.

${y'} - {y} = 8 \, \cos\left(4 \, t\right) e^{t}$

$y= k e^{t} + 2 \, e^{t} \sin\left(4 \, t\right)$

## C2 - Non-homogeneous first-order linear ODE (ver. 49)

Find the general solution to the given ODE.

${y'} + 3 \, {y} = -6 \, e^{\left(-3 \, t\right)} \sin\left(-2 \, t\right)$

$y= k e^{\left(-3 \, t\right)} - 3 \, \cos\left(-2 \, t\right) e^{\left(-3 \, t\right)}$

## C2 - Non-homogeneous first-order linear ODE (ver. 50)

Find the general solution to the given ODE.

${y'} + 3 \, {y} = -2 \, e^{\left(-3 \, t\right)}$

$y= k e^{\left(-3 \, t\right)} - 2 \, t e^{\left(-3 \, t\right)}$