What is the solution for y^{''}-4y^'-5y=9e^2t ?

The solution for y^{''}-4y^'-5y=9e^2t is y=c_{1}e^{5t}+c_{2}e^{-t}-(9e^2t)/5+(36e^2)/(25)

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y^{''}-4y^'-5y=9e^2t

y^{^{''}} - 4 y^{^{'}} - 5 y = 9 e^{2} t

y = c_{1} e^{5 t} + c_{2} e^{- t} - \frac{9 e ^{2} t}{5} + \frac{36 e ^{2}}{25}

Solution steps

y^{''} (t) - 4 y^{'} (t) - 5 y = 9 e^{2} t

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- t} - \frac{9 e ^{2} t}{5} + \frac{36 e ^{2}}{25}

y = c_{1} e^{5 t} + c_{2} e^{- t} - \frac{9 e ^{2} t}{5} + \frac{36 e ^{2}}{25}

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What is the solution for y^{''}-4y^'-5y=9e^2t ?
The solution for y^{''}-4y^'-5y=9e^2t is y=c_{1}e^{5t}+c_{2}e^{-t}-(9e^2t)/5+(36e^2)/(25)