What is the solution for (d^2y)/(dx^2)+y=x^2 ?

The solution for (d^2y)/(dx^2)+y=x^2 is y=c_{1}cos(x)+c_{2}sin(x)+x^2-2

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(d^2y)/(dx^2)+y=x^2

\frac{d ^{2} y}{d x ^{2}} + y = x^{2}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + y = x^{2}

Solve linear ODE:

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

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

y^{^{''}} + y = - 16 cos (3 x)

4 y^{^{''}} - y = e^{\frac{x}{2}} + 7

y^{^{''}} + 6 y^{^{'}} + 13 y = e^{- 3 x} cos (2 x)

y^{^{''}} + y^{^{'}} - 6 y = 2 x^{2} + 1

y^{^{''}} + 4 y = 3 sin (3 t)

What is the solution for (d^2y)/(dx^2)+y=x^2 ?
The solution for (d^2y)/(dx^2)+y=x^2 is y=c_{1}cos(x)+c_{2}sin(x)+x^2-2