What is the solution for (d^2x)/(dt^2)+(dx)/(dt)=5t ?

The solution for (d^2x)/(dt^2)+(dx)/(dt)=5t is x=c_{1}+c_{2}e^{-t}+(5t^2)/2-5t

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(d^2x)/(dt^2)+(dx)/(dt)=5t

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} = 5 t

x = c_{1} + c_{2} e^{- t} + \frac{5 t ^{2}}{2} - 5 t

Solution steps

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} = 5 t

Solve linear ODE:

x = c_{1} + c_{2} e^{- t} + \frac{5 t ^{2}}{2} - 5 t

x = c_{1} + c_{2} e^{- t} + \frac{5 t ^{2}}{2} - 5 t

3 y^{^{''}} + 2 y^{^{'}} - y = 23

y^{^{''}} - y^{^{'}} - 6 y = 45 cos (3 x)

y^{^{''}} + 4 y^{^{'}} + 3 y = 8 e^{- 2 x}

y^{^{''}} + 3 y^{^{'}} + 2 y = 3 e^{2 t}

y^{^{''}} - 8 y^{^{'}} + 16 y = e^{- x}

What is the solution for (d^2x)/(dt^2)+(dx)/(dt)=5t ?
The solution for (d^2x)/(dt^2)+(dx)/(dt)=5t is x=c_{1}+c_{2}e^{-t}+(5t^2)/2-5t