What is the solution for y^{''}+9y=sin(3x)+e^{2x} ?

The solution for y^{''}+9y=sin(3x)+e^{2x} is y=c_{1}cos(3x)+c_{2}sin(3x)-(xcos(3x))/6+1/13 e^{2x}

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y^{''}+9y=sin(3x)+e^{2x}

y^{^{''}} + 9 y = sin (3 x) + e^{2 x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x cos ( 3 x )}{6} + \frac{1}{13} e^{2 x}

Solution steps

y^{''} (x) + 9 y = sin (3 x) + e^{2 x}

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x cos ( 3 x )}{6} + \frac{1}{13} e^{2 x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x cos ( 3 x )}{6} + \frac{1}{13} e^{2 x}

y^{^{''}} - y^{^{'}} - 2 y = 8 x + 5

y^{^{''}} - 2 y^{^{'}} - 3 y = 2 e^{3 t}

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

y^{^{''}} - 8 y^{^{'}} - 4 y - 2 = 10 x^{2} - 2 x e^{2}

y^{^{''}} - y^{^{'}} - 6 y = 22 cos (3 x)

What is the solution for y^{''}+9y=sin(3x)+e^{2x} ?
The solution for y^{''}+9y=sin(3x)+e^{2x} is y=c_{1}cos(3x)+c_{2}sin(3x)-(xcos(3x))/6+1/13 e^{2x}