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

The solution for y^{''}+2y=-18x^2e^2x is y=c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x)-9e^2x^3+27e^2x

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

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

y = c_{1} cos (2 x) + c_{2} sin (2 x) - 9 e^{2} x^{3} + 27 e^{2} x

Solution steps

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

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) - 9 e^{2} x^{3} + 27 e^{2} x

y = c_{1} cos (2 x) + c_{2} sin (2 x) - 9 e^{2} x^{3} + 27 e^{2} x

\frac{d}{d x} (- \frac{9}{( 1 + 3 x ) ^{2}})

y = x^{3} - 3 x^{2} + 3 x, y = x

\frac{d}{d x} (x^{2} - 7 x + 12)

\frac{d}{d x} (\frac{e ^{\frac{x}{2}}}{x + 1})

\int \frac{sin ( x )}{cos ( x ) + sin ( x )} d x

What is the solution for y^{''}+2y=-18x^2e^2x ?
The solution for y^{''}+2y=-18x^2e^2x is y=c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x)-9e^2x^3+27e^2x