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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\int_{0}^{y} y e^{- y} d y

\frac{d y}{d t} y = (2 t - 1) (3 t - 4)^{- 1}

lo g_{5} (2 x)

\int_{- \frac{π}{4}}^{\frac{π}{4}} tan (x) d x

\int 2 sin (x) cos^{2} (x) d x

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