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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

ln (t^{2} + 1)

x \to 0 lim (\frac{x ^{3}}{x})

\int \frac{2 x ^{4} + 7 x ^{3} - x}{x ^{3}} d x

\frac{\partial}{\partial t} (x e^{2 t} - 4 x)

\int_{- 1}^{2} 2^{x} d x

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