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

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

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-9y^{''}+y=9t-4e^t+9

- 9 y^{^{''}} + y = 9 t - 4 e^{t} + 9

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 3 y = 2 e^{x}

y^{^{''}} - y = \frac{1}{( e ^{x} + 1 )}

y^{^{''}} + 2 y = 1 + e^{x}

\frac{d ^{4} y}{d t ^{4}} - 4 y^{^{''}} = t^{2} + e^{t}

y^{^{''}} - 6 y^{^{'}} + 25 y = sin (\frac{t}{2}) + e^{- t} t

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