What is the solution for y^{''}+2y^'=2x+7-e^{-2x} ?

The solution for y^{''}+2y^'=2x+7-e^{-2x} is y=c_{1}+c_{2}e^{-2x}+(x^2+e^{-2x}x)/2+3x

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

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

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

Solution steps

y^{''} (x) + 2 y^{'} (x) = 2 x + 7 - e^{- 2 x}

Solve linear ODE:

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

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

\int_{- 1}^{1} (x^{2} - 1)^{2} d x

\int \frac{x - 1}{x} d x

6 x y^{^{'}} + y = x^{4}

\frac{d}{d x} (e^{x} (3 x + 1)^{3})

\frac{d}{d x} (\frac{e ^{x}}{y})

What is the solution for y^{''}+2y^'=2x+7-e^{-2x} ?
The solution for y^{''}+2y^'=2x+7-e^{-2x} is y=c_{1}+c_{2}e^{-2x}+(x^2+e^{-2x}x)/2+3x