What is the solution for y^{''}-2y^'=2x+9-e^{-2x} ?

The solution for y^{''}-2y^'=2x+9-e^{-2x} is y=c_{1}e^{2x}+c_{2}-(x^2)/2-5x-1/8 e^{-2x}

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y^{''}-2y^'=2x+9-e^{-2x}

y^{^{''}} - 2 y^{^{'}} = 2 x + 9 - e^{- 2 x}

y = c_{1} e^{2 x} + c_{2} - \frac{x ^{2}}{2} - 5 x - \frac{1}{8} e^{- 2 x}

Solution steps

y^{''} (x) - 2 y^{'} (x) = 2 x + 9 - e^{- 2 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} - \frac{x ^{2}}{2} - 5 x - \frac{1}{8} e^{- 2 x}

y = c_{1} e^{2 x} + c_{2} - \frac{x ^{2}}{2} - 5 x - \frac{1}{8} e^{- 2 x}

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

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

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

y^{^{''}} - \frac{25}{21} y^{^{'}} + \frac{5}{18} y = \frac{355}{21}

y^{^{''}} + 3 y^{^{'}} - 40 y = - 132 t + 80 t^{2}

What is the solution for y^{''}-2y^'=2x+9-e^{-2x} ?
The solution for y^{''}-2y^'=2x+9-e^{-2x} is y=c_{1}e^{2x}+c_{2}-(x^2)/2-5x-1/8 e^{-2x}