What is the solution for xy^'+2y=-2e^x ?

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

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xy^'+2y=-2e^x

x y^{^{'}} + 2 y = - 2 e^{x}

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

Solution steps

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

Solve linear ODE:

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

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

x \to - 3 lim (\frac{7}{x + 3})

y^{^{'}} = t^{2} - y

\frac{d}{d x} (arccos (\frac{3}{x}))

7 y^{^{''}} + 4 y^{^{'}} = 0

\int (t^{2} + 2)^{3} d t

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