What is the solution for (d^2x)/(dt^2)+(dx)/(dt)=6t ?

The solution for (d^2x)/(dt^2)+(dx)/(dt)=6t is x=c_{1}+c_{2}e^{-t}+3t^2-6t

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(d^2x)/(dt^2)+(dx)/(dt)=6t

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} = 6 t

x = c_{1} + c_{2} e^{- t} + 3 t^{2} - 6 t

Solution steps

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} = 6 t

Solve linear ODE:

x = c_{1} + c_{2} e^{- t} + 3 t^{2} - 6 t

x = c_{1} + c_{2} e^{- t} + 3 t^{2} - 6 t

y^{^{''}} + 2 y^{^{'}} - 3 y = - 15 x^{2} + 26 x - 3

y^{^{''}} + 6 y^{^{'}} + 5 y = 5 x + 1

y^{^{''}} + 17 y^{^{'}} + 72 y = 4 x e^{x}

y^{^{''}} + 25 y = 4 sec (5 x)

\frac{d ^{2} v}{d x ^{2}} - k^{2} v = k^{2} n

What is the solution for (d^2x)/(dt^2)+(dx)/(dt)=6t ?
The solution for (d^2x)/(dt^2)+(dx)/(dt)=6t is x=c_{1}+c_{2}e^{-t}+3t^2-6t