What is the solution for y^{''}-6y^'-27y=-57t+54t^2 ?

The solution for y^{''}-6y^'-27y=-57t+54t^2 is y=c_{1}e^{9t}+c_{2}e^{-3t}-2t^2+3t-22/27

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y^{''}-6y^'-27y=-57t+54t^2

y^{^{''}} - 6 y^{^{'}} - 27 y = - 57 t + 54 t^{2}

y = c_{1} e^{9 t} + c_{2} e^{- 3 t} - 2 t^{2} + 3 t - \frac{22}{27}

Solution steps

y^{''} (t) - 6 y^{'} (t) - 27 y = - 57 t + 54 t^{2}

Solve linear ODE:

y = c_{1} e^{9 t} + c_{2} e^{- 3 t} - 2 t^{2} + 3 t - \frac{22}{27}

y = c_{1} e^{9 t} + c_{2} e^{- 3 t} - 2 t^{2} + 3 t - \frac{22}{27}

y^{^{''}} + 15 y^{^{'}} + 56 y = 112 x^{2} + 60 x + 4 + 72 e^{x}

(d^{3} - 3 d^{2} + 4 d - 2) y = e^{x} + cos (x) + x

y^{^{''}} - y = 2 e^{x} sinh (x)

y^{^{''}} + 16 y = 0.5 sin (4 t), y (0) = 0.5

(D^{2} + 9) y = 81 x^{2} + (14 cos (x))

What is the solution for y^{''}-6y^'-27y=-57t+54t^2 ?
The solution for y^{''}-6y^'-27y=-57t+54t^2 is y=c_{1}e^{9t}+c_{2}e^{-3t}-2t^2+3t-22/27