What is the solution for y^{''}+2y=-18xe^{2x} ?

The solution for y^{''}+2y=-18xe^{2x} is y=c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x)-3xe^{2x}+2e^{2x}

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y^{''}+2y=-18xe^{2x}

y^{^{''}} + 2 y = - 18 x e^{2 x}

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

Solution steps

y^{''} (x) + 2 y = - 18 x e^{2 x}

Solve linear ODE:

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

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

What is the solution for y^{''}+2y=-18xe^{2x} ?
The solution for y^{''}+2y=-18xe^{2x} is y=c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x)-3xe^{2x}+2e^{2x}