What is the solution for y^{''}+y^'-72y=-220t+144t^2 ?

The solution for y^{''}+y^'-72y=-220t+144t^2 is y=c_{1}e^{8t}+c_{2}e^{-9t}-2t^2+3t-1/72

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y^{''}+y^'-72y=-220t+144t^2

y^{^{''}} + y^{^{'}} - 72 y = - 220 t + 144 t^{2}

y = c_{1} e^{8 t} + c_{2} e^{- 9 t} - 2 t^{2} + 3 t - \frac{1}{72}

Solution steps

y^{''} (t) + y^{'} (t) - 72 y = - 220 t + 144 t^{2}

Solve linear ODE:

y = c_{1} e^{8 t} + c_{2} e^{- 9 t} - 2 t^{2} + 3 t - \frac{1}{72}

y = c_{1} e^{8 t} + c_{2} e^{- 9 t} - 2 t^{2} + 3 t - \frac{1}{72}

y^{^{''}} - 10 y^{^{'}} + 25 y = 8 e^{5 x}

y^{^{''}} - y^{^{'}} - 2 y = 5 x + 5

y^{^{''}} - 6 y^{^{'}} + 5 y = 3 e^{2 t}, y (0) = 2, y^{^{'}} (0) = 3

y^{^{'''}} + 4 y^{^{'}} = e^{x} + 3 sin (2 x) + 1

5 y^{^{''}} + 6 y^{^{'}} + 25 y = 4 cos (2 t)

What is the solution for y^{''}+y^'-72y=-220t+144t^2 ?
The solution for y^{''}+y^'-72y=-220t+144t^2 is y=c_{1}e^{8t}+c_{2}e^{-9t}-2t^2+3t-1/72