What is the solution for (d^2y)/(dx^2)+2(dy)/(dx)=2x+5-e^{-2x} ?

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

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(d^2y)/(dx^2)+2(dy)/(dx)=2x+5-e^{-2x}

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} = 2 x + 5 - e^{- 2 x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} = 2 x + 5 - e^{- 2 x}

Solve linear ODE:

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

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

D (x) = (x - 8)^{2}, S (x) = x^{2} + 2 x + 28

y^{^{''}} + 2 y^{^{'}} = x^{2} + 1

y^{^{''}} - y^{^{'}} - 20 y = 27 e^{- 4 c}

(D - 2)^{2} y = 8 e^{2 x}

y^{^{''}} - 10 y^{^{'}} + 25 y = 102 t^{2} e^{5 t}

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