What is the solution for y^{''}+y^'-2y=14+2x-2x^2 ?

The solution for y^{''}+y^'-2y=14+2x-2x^2 is y=c_{1}e^x+c_{2}e^{-2x}+x^2-6

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y^{''}+y^'-2y=14+2x-2x^2

y^{^{''}} + y^{^{'}} - 2 y = 14 + 2 x - 2 x^{2}

y = c_{1} e^{x} + c_{2} e^{- 2 x} + x^{2} - 6

Solution steps

y^{''} (x) + y^{'} (x) - 2 y = 14 + 2 x - 2 x^{2}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + x^{2} - 6

y = c_{1} e^{x} + c_{2} e^{- 2 x} + x^{2} - 6

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

(d^{2} - 4 d + 4) \cdot y = 12 \cdot (1 + x)^{2} \cdot e^{2 x}

y^{^{'''}} - y^{^{'}} = 4 e^{- x} + 3 e^{2} x

(d^{2} + 4) y = e^{3} x

(d - 1)^{2} \cdot y = sin (x) \cdot x^{2} \cdot e^{x}

What is the solution for y^{''}+y^'-2y=14+2x-2x^2 ?
The solution for y^{''}+y^'-2y=14+2x-2x^2 is y=c_{1}e^x+c_{2}e^{-2x}+x^2-6