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

The solution for y^{''}+y^'-2y=4x^2 is y=c_{1}e^x+c_{2}e^{-2x}-2x^2-2x-3

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y^{''}+y^'-2y=4x^2

y^{^{''}} + y^{^{'}} - 2 y = 4 x^{2}

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 5 y^{^{'}} + 6 y = 4 x e^{2 x}

y^{^{''}} - y^{^{'}} - 6 y = - e^{x} + 12 x

y^{^{''}} - 9 y = sinh (3 x)

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

y^{^{''}} + 6 y^{^{'}} - 7 y = 3 e^{2 x} - e^{- x}

What is the solution for y^{''}+y^'-2y=4x^2 ?
The solution for y^{''}+y^'-2y=4x^2 is y=c_{1}e^x+c_{2}e^{-2x}-2x^2-2x-3