What is the solution for y^'+y=e^{-x}sqrt(x) ?

The solution for y^'+y=e^{-x}sqrt(x) is y=(2x^{3/2})/(3e^x)+(c_{1})/(e^x)

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

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

y = \frac{2 x ^{\frac{3}{2}}}{3 e ^{x}} + \frac{c _{1}}{e ^{x}}

Solution steps

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

Solve linear ODE:

y = \frac{2 x ^{\frac{3}{2}}}{3 e ^{x}} + \frac{c _{1}}{e ^{x}}

y = \frac{2 x ^{\frac{3}{2}}}{3 e ^{x}} + \frac{c _{1}}{e ^{x}}

\int \frac{2 x ^{2} + 7 x + 2}{( x ^{2} + 1 ) ^{2}} d x

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

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

\int \frac{arcsin ( x )}{x} d x

y^{^{''}} + 16 y^{^{'}} + 80 y = 0

What is the solution for y^'+y=e^{-x}sqrt(x) ?
The solution for y^'+y=e^{-x}sqrt(x) is y=(2x^{3/2})/(3e^x)+(c_{1})/(e^x)