What is the solution for y^{''}-y^'-20y=72e^{2t} ?

The solution for y^{''}-y^'-20y=72e^{2t} is y=c_{1}e^{5t}+c_{2}e^{-4t}-4e^{2t}

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y^{''}-y^'-20y=72e^{2t}

y^{^{''}} - y^{^{'}} - 20 y = 72 e^{2 t}

y = c_{1} e^{5 t} + c_{2} e^{- 4 t} - 4 e^{2 t}

Solution steps

y^{''} (t) - y^{'} (t) - 20 y = 72 e^{2 t}

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- 4 t} - 4 e^{2 t}

y = c_{1} e^{5 t} + c_{2} e^{- 4 t} - 4 e^{2 t}

y^{^{''}} - y = t, y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} - 2 y + 5 = 0

y^{^{'''}} - 2 y^{^{''}} + 3 y^{^{'}} - 2 y = 2 e^{x}

y^{^{''}} + y - 5 = e^{2 x} - 3 cos (3 x)

y^{^{'''}} - 18 y^{^{''}} + 864 y = e^{12 x}

What is the solution for y^{''}-y^'-20y=72e^{2t} ?
The solution for y^{''}-y^'-20y=72e^{2t} is y=c_{1}e^{5t}+c_{2}e^{-4t}-4e^{2t}