What is the solution for y^{''}+ay^'=e^{3t} ?

The solution for y^{''}+ay^'=e^{3t} is y=c_{1}+c_{2}e^{-at}+(e^{3t})/(3(a+3))

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y^{''}+ay^'=e^{3t}

y^{^{''}} + a y^{^{'}} = e^{3 t}

y = c_{1} + c_{2} e^{- a t} + \frac{e ^{3 t}}{3 ( a + 3 )}

Solution steps

y^{''} (t) + a y^{'} (t) = e^{3 t}

Solve linear ODE:

y = c_{1} + c_{2} e^{- a t} + \frac{e ^{3 t}}{3 ( a + 3 )}

y = c_{1} + c_{2} e^{- a t} + \frac{e ^{3 t}}{3 ( a + 3 )}

What is the solution for y^{''}+ay^'=e^{3t} ?
The solution for y^{''}+ay^'=e^{3t} is y=c_{1}+c_{2}e^{-at}+(e^{3t})/(3(a+3))