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

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

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y^{''}+y=2+x^2

y^{^{''}} + y = 2 + x^{2}

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

Solution steps

y^{''} (x) + y = 2 + x^{2}

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 x + 1

y^{^{''}} - 2 y^{^{'}} = 12 x^{2}

y^{^{''}} - 6 y^{^{'}} + 9 y = 5 x^{- 2 x}

y^{^{''}} - 3 y^{^{'}} - 5 = e^{2 x} - 3 cos (3 x)

y^{^{''}} + 3 y^{^{'}} + 2 = sin (e^{x})

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