What is the solution for y^{''}+9y=12xe^{2x} ?

The solution for y^{''}+9y=12xe^{2x} is y=c_{1}cos(3x)+c_{2}sin(3x)+(12e^{2x}x)/(13)-48/169 e^{2x}

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y^{''}+9y=12xe^{2x}

y^{^{''}} + 9 y = 12 x e^{2 x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{12 e ^{2 x} x}{13} - \frac{48}{169} e^{2 x}

Solution steps

y^{''} (x) + 9 y = 12 x e^{2 x}

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{12 e ^{2 x} x}{13} - \frac{48}{169} e^{2 x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{12 e ^{2 x} x}{13} - \frac{48}{169} e^{2 x}

y^{^{''}} - y^{^{'}} - 2 y = 7 e^{2 x} - 3 e^{x}

y^{^{''}} + y^{^{'}} = 4 x + 10 sin (x)

y^{^{''}} - 4 y^{^{'}} + 3 y = e t - 2 t + 3

y^{^{''}} - 3 y^{^{'}} = 2 x + 5 - e^{3 x}

y^{^{''}} - y^{^{'}} - 6 y = 2 e^{3 t}

What is the solution for y^{''}+9y=12xe^{2x} ?
The solution for y^{''}+9y=12xe^{2x} is y=c_{1}cos(3x)+c_{2}sin(3x)+(12e^{2x}x)/(13)-48/169 e^{2x}