What is the solution for y^{''}+3y^'-18y=-66t+36t^2 ?

The solution for y^{''}+3y^'-18y=-66t+36t^2 is y=c_{1}e^{3t}+c_{2}e^{-6t}-2t^2+3t+5/18

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y^{''}+3y^'-18y=-66t+36t^2

y^{^{''}} + 3 y^{^{'}} - 18 y = - 66 t + 36 t^{2}

y = c_{1} e^{3 t} + c_{2} e^{- 6 t} - 2 t^{2} + 3 t + \frac{5}{18}

Solution steps

y^{''} (t) + 3 y^{'} (t) - 18 y = - 66 t + 36 t^{2}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 6 t} - 2 t^{2} + 3 t + \frac{5}{18}

y = c_{1} e^{3 t} + c_{2} e^{- 6 t} - 2 t^{2} + 3 t + \frac{5}{18}

y^{^{''}} + 3 y^{^{'}} + 2 y = 4 x^{2}

y^{^{''}} + 2 y^{^{'}} + 5 y = 3 e^{- 2 t}

(D^{2} - 4 D + 13) y = 24 e^{2 x} cos (3 x)

y^{^{''}} - 2 y^{^{'}} + 10 y = 3 e^{x} tan (3 x)

y^{^{''}} + 4 y^{^{'}} + 4 y = 7 e^{- 2 t}

What is the solution for y^{''}+3y^'-18y=-66t+36t^2 ?
The solution for y^{''}+3y^'-18y=-66t+36t^2 is y=c_{1}e^{3t}+c_{2}e^{-6t}-2t^2+3t+5/18