What is the solution for y^{''}+9y=e^{-2x} ?

The solution for y^{''}+9y=e^{-2x} is y=c_{1}cos(3x)+c_{2}sin(3x)+1/13 e^{-2x}

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y^{''}+9y=e^{-2x}

y^{^{''}} + 9 y = e^{- 2 x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{13} e^{- 2 x}

Solution steps

y^{''} (x) + 9 y = e^{- 2 x}

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{13} e^{- 2 x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{13} e^{- 2 x}

y^{^{'''}} + 3 y^{^{''}} + 2 y^{^{'}} = x^{2} + 4 x + 8

y^{^{''}} + 4 y^{^{'}} + 4 y = - 2 sin (3 x)

x^{^{''}} - 2 x^{^{'}} + x = 2000 t^{2} - 150 e^{t}

y^{^{'''}} + 10 y^{^{''}} + 25 y^{^{'}} = e^{x}

y^{^{''}} + 4 y = (x^{2} - 3) sin (2 x)

What is the solution for y^{''}+9y=e^{-2x} ?
The solution for y^{''}+9y=e^{-2x} is y=c_{1}cos(3x)+c_{2}sin(3x)+1/13 e^{-2x}