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

The solution for y^{''}+9y=xe^{2x} is y=c_{1}cos(3x)+c_{2}sin(3x)+(e^{2x}x)/(13)-4/169 e^{2x}

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y^{''}+9y=xe^{2x}

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

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{e ^{2 x} x}{13} - \frac{4}{169} e^{2 x}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{e ^{2 x} x}{13} - \frac{4}{169} e^{2 x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{e ^{2 x} x}{13} - \frac{4}{169} e^{2 x}

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What is the solution for y^{''}+9y=xe^{2x} ?
The solution for y^{''}+9y=xe^{2x} is y=c_{1}cos(3x)+c_{2}sin(3x)+(e^{2x}x)/(13)-4/169 e^{2x}