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

The solution for (x+1)y^'+(x+2)y=2xe^{-x} is y=(x^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=2xe^{-x}

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

y = \frac{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 = 2 x e^{- x}

Solve linear ODE:

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

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

x^{\frac{2}{3}} + y^{\frac{2}{3}} = 10, (27, 1)

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

6 x^{4} - 9 x y - 7 y^{2} = 104, (- 2, 2)

n = 1 \sum \infty \frac{- n}{n ^{2} + 1}

x \to 2 lim (3 x^{2} - 5 x + 2)

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