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

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

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

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

y = c_{1} + c_{2} e^{- 2 x} + \frac{( - e + 9 ) x}{2}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + \frac{( - e + 9 ) x}{2}

y = c_{1} + c_{2} e^{- 2 x} + \frac{( - e + 9 ) x}{2}

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 t^{2} + 4 t e^{2 t} + t sin (2 t)

y^{^{''}} - 12 y^{^{'}} + 36 y = (x + 1) e^{x}

y^{^{''}} + 2 y^{^{'}} + y = \frac{e ^{- t}}{t + 1}

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

4 y^{^{''}} + 16 y = sin (x) + 2 cos (x)

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