What is the solution for y^{''}+9y=sin(3x)+e^{-x} ?

The solution for y^{''}+9y=sin(3x)+e^{-x} is y=c_{1}cos(3x)+c_{2}sin(3x)-(xcos(3x))/6+1/10 e^{-x}

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y^{''}+9y=sin(3x)+e^{-x}

y^{^{''}} + 9 y = sin (3 x) + e^{- x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x cos ( 3 x )}{6} + \frac{1}{10} e^{- x}

Solution steps

y^{''} (x) + 9 y = sin (3 x) + e^{- x}

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x cos ( 3 x )}{6} + \frac{1}{10} e^{- x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x cos ( 3 x )}{6} + \frac{1}{10} e^{- x}

What is the solution for y^{''}+9y=sin(3x)+e^{-x} ?
The solution for y^{''}+9y=sin(3x)+e^{-x} is y=c_{1}cos(3x)+c_{2}sin(3x)-(xcos(3x))/6+1/10 e^{-x}