What is the solution for y^{''}-9y=54t^2 ?

The solution for y^{''}-9y=54t^2 is y=c_{1}e^{3t}+c_{2}e^{-3t}-6t^2-4/3

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y^{''}-9y=54t^2

y^{^{''}} - 9 y = 54 t^{2}

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - 6 t^{2} - \frac{4}{3}

Solution steps

y^{''} (t) - 9 y = 54 t^{2}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - 6 t^{2} - \frac{4}{3}

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - 6 t^{2} - \frac{4}{3}

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

y^{^{''}} + 4 y = t^{2} + 4 e^{t}, y (0) = 0, y^{^{'}} (0) = 9

y^{^{''}} + 4 y = t^{2} + 4 e^{t}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 10 y^{^{'}} + 25 y = t^{- 3} e^{5 t}

y^{^{''}} + k^{2} y = k_{2} \cdot sin (k x)

What is the solution for y^{''}-9y=54t^2 ?
The solution for y^{''}-9y=54t^2 is y=c_{1}e^{3t}+c_{2}e^{-3t}-6t^2-4/3