What is the solution for y^{''}+9y=e^x ?

The solution for y^{''}+9y=e^x is y=c_{1}cos(3x)+c_{2}sin(3x)+1/10 e^x

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y^{''}+9y=e^x

y^{^{''}} + 9 y = e^{x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{10} e^{x}

Solution steps

y^{''} (x) + 9 y = e^{x}

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{10} e^{x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{10} e^{x}

y^{^{''''}} + 8 y^{^{''}} + 16 y = 48 + cos (4 t)

y^{^{''}} + 16 y = 32 t

y^{^{''}} + 4 y^{^{'}} + 6 y = 4 e^{- 2 x} cos (x)

y^{^{''}} + 2 y^{^{'}} + 5 y = 24 e^{- t} cos (2 t)

y^{^{''}} - 5 y^{^{'}} + 4 y = \frac{6}{1 + e ^{- 2 x}}

What is the solution for y^{''}+9y=e^x ?
The solution for y^{''}+9y=e^x is y=c_{1}cos(3x)+c_{2}sin(3x)+1/10 e^x