What is the solution for y^'+y=x*e^{-x}+1 ?

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

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y^'+y=x*e^{-x}+1

y^{^{'}} + y = x \cdot e^{- x} + 1

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

Solution steps

y^{'} (x) + y = x \cdot 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}}

2 x^{3} + 36 x^{2} + 210 x + 11

\int a x^{3} d x

\int \frac{6 x ^{2} + 4 x - 30}{x ^{3} + 5 x ^{2} + 6 x} d x

\int_{3}^{4} \frac{1}{x ^{2} - 4} d x

f (x) = 5 x^{2} - 3 x + 7

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