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

The solution for y^{''}+y^'-2y=2+2x+2x^2 is y=c_{1}e^x+c_{2}e^{-2x}-x^2-2x-3

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

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

y = c_{1} e^{x} + c_{2} e^{- 2 x} - x^{2} - 2 x - 3

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} - x^{2} - 2 x - 3

y = c_{1} e^{x} + c_{2} e^{- 2 x} - x^{2} - 2 x - 3

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

y^{^{''}} - 3 y = - 48 x^{2} e^{3 x}

y^{^{''}} + 16 y = 3 cos (4 t)

y^{^{''}} - 4 y^{^{'}} + 5 y = cos^{2} (x)

2 y^{^{''}} - 6 y = 2 x^{2} - x^{2} - x + 3

What is the solution for y^{''}+y^'-2y=2+2x+2x^2 ?
The solution for y^{''}+y^'-2y=2+2x+2x^2 is y=c_{1}e^x+c_{2}e^{-2x}-x^2-2x-3