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

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

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

linear

\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^{^{''}} + 9 y = 9 cos^{3} (3 x)

y^{^{''}} + 2 y^{^{'}} = 49 e^{x} sin (2 x)

y^{^{''}} + 2 y^{^{'}} + 1 = t e^{t} sin (t)

y^{^{''''}} + 2 y^{^{''}} + y = 3 t + 10

y^{^{''}} - 5 y^{^{'}} + 6 y = \frac{e ^{2 x}}{1 + e ^{x}}

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