What is the solution for y^{''}+16y=xe^{3x} ?

The solution for y^{''}+16y=xe^{3x} is y=c_{1}cos(4x)+c_{2}sin(4x)+(e^{3x}x)/(25)-6/625 e^{3x}

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y^{''}+16y=xe^{3x}

y^{^{''}} + 16 y = x e^{3 x}

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{e ^{3 x} x}{25} - \frac{6}{625} e^{3 x}

Solution steps

y^{''} (x) + 16 y = x e^{3 x}

Solve linear ODE:

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{e ^{3 x} x}{25} - \frac{6}{625} e^{3 x}

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{e ^{3 x} x}{25} - \frac{6}{625} e^{3 x}

What is the solution for y^{''}+16y=xe^{3x} ?
The solution for y^{''}+16y=xe^{3x} is y=c_{1}cos(4x)+c_{2}sin(4x)+(e^{3x}x)/(25)-6/625 e^{3x}