What is the solution for y^{''}+2y^'=2x+5-2e^{-2x} ?

The solution for y^{''}+2y^'=2x+5-2e^{-2x} is y=c_{1}+c_{2}e^{-2x}+(x^2)/2+2x+e^{-2x}x

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 25 y = x + sin (x)

y^{^{''}} - 4 y = 8 e^{3 x}

x^{^{''}} + 25 x = 32 cos (3 t)

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 6

2 y^{^{''}} + y^{^{'}} + 3 y = 3 cos (3 t) + 2 sin (3 t)

What is the solution for y^{''}+2y^'=2x+5-2e^{-2x} ?
The solution for y^{''}+2y^'=2x+5-2e^{-2x} is y=c_{1}+c_{2}e^{-2x}+(x^2)/2+2x+e^{-2x}x