What is the solution for (dy)/(dx)+y=xe^{-x}+1 ?

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

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(dy)/(dx)+y=xe^{-x}+1

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

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

Solution steps

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

Solve linear ODE:

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

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

n = 0 \sum \infty \frac{1}{n ( n + 2 )}

x \to 5 lim (x^{2} - 25)

\frac{d}{d x} (x (x^{2} + 1)^{2})

\int_{0}^{1} \frac{4 x + 6}{( x + 1 ) ^{2}} d x

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

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