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

The solution for y^{''}+2y^'=2x+5-e^-2x is y=c_{1}+c_{2}e^{-2x}+((1-e^-)x^2)/2+((e^-+4)x)/2

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

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

y = c_{1} + c_{2} e^{- 2 x} + \frac{( 1 - e ^{-} ) x ^{2}}{2} + \frac{( e ^{-} + 4 ) x}{2}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + \frac{( 1 - e ^{-} ) x ^{2}}{2} + \frac{( e ^{-} + 4 ) x}{2}

y = c_{1} + c_{2} e^{- 2 x} + \frac{( 1 - e ^{-} ) x ^{2}}{2} + \frac{( e ^{-} + 4 ) x}{2}

\frac{d}{d x} (\frac{2 x ^{3} - 7}{x ^{2}})

\frac{d y}{d x} = 100 - y

x \to \infty lim ((1 + \frac{1}{2 x + 1})^{x^{2 - 3}})

\int_{0}^{1} (x^{2} - 3 x + 6) d x

x \to 0 lim (+ (x sin (\frac{1}{x})))

What is the solution for y^{''}+2y^'=2x+5-e^-2x ?
The solution for y^{''}+2y^'=2x+5-e^-2x is y=c_{1}+c_{2}e^{-2x}+((1-e^-)x^2)/2+((e^-+4)x)/2