What is the solution for y^{''}+6y^'-27y=-105t+54t^2 ?

The solution for y^{''}+6y^'-27y=-105t+54t^2 is y=c_{1}e^{3t}+c_{2}e^{-9t}-2t^2+3t+14/27

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y^{''}+6y^'-27y=-105t+54t^2

y^{^{''}} + 6 y^{^{'}} - 27 y = - 105 t + 54 t^{2}

y = c_{1} e^{3 t} + c_{2} e^{- 9 t} - 2 t^{2} + 3 t + \frac{14}{27}

Solution steps

y^{''} (t) + 6 y^{'} (t) - 27 y = - 105 t + 54 t^{2}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 9 t} - 2 t^{2} + 3 t + \frac{14}{27}

y = c_{1} e^{3 t} + c_{2} e^{- 9 t} - 2 t^{2} + 3 t + \frac{14}{27}

What is the solution for y^{''}+6y^'-27y=-105t+54t^2 ?
The solution for y^{''}+6y^'-27y=-105t+54t^2 is y=c_{1}e^{3t}+c_{2}e^{-9t}-2t^2+3t+14/27