What is the solution for (x+1)y^'+(x+2)y=8xe^{-x} ?

The solution for (x+1)y^'+(x+2)y=8xe^{-x} is y=(4x^2)/(e^x(x+1))+(c_{1})/(e^{x+c_{1)}x+e^{x+c_{1}}}

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(x+1)y^'+(x+2)y=8xe^{-x}

(x + 1) y^{^{'}} + (x + 2) y = 8 x e^{- x}

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

Solution steps

(x + 1) y^{'} (x) + (x + 2) y = 8 x e^{- x}

Solve linear ODE:

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

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

\int 8 x^{3} e^{x^{4}} d x

8 x sin (x)

1 - x^{2}, 13 - 7 x

\frac{\partial}{\partial x} (e^{8 x} cos (5 y))

\frac{d}{d x} (5 csc (x))

What is the solution for (x+1)y^'+(x+2)y=8xe^{-x} ?
The solution for (x+1)y^'+(x+2)y=8xe^{-x} is y=(4x^2)/(e^x(x+1))+(c_{1})/(e^{x+c_{1)}x+e^{x+c_{1}}}