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

The solution for y^{''}-y=2+x^2 is y=c_{1}e^x+c_{2}e^{-x}-x^2-4

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

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

y = c_{1} e^{x} + c_{2} e^{- x} - x^{2} - 4

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} - x^{2} - 4

y = c_{1} e^{x} + c_{2} e^{- x} - x^{2} - 4

y^{^{''}} + b y^{^{'}} + cy = e^{x} sin (x)

10 y^{^{''}} + 50 y^{^{'}} + 57.6 y = cos (x)

y^{^{''}} + y = 5 sin (4 x)

12 y^{^{''}} + 5 y^{^{'}} - 3 y = e^{x}

y^{^{''}} - 3 y^{^{'}} - 2 y = 9 e^{- x}

What is the solution for y^{''}-y=2+x^2 ?
The solution for y^{''}-y=2+x^2 is y=c_{1}e^x+c_{2}e^{-x}-x^2-4