What is the solution for x^2(dy)/(dx)+(x^2+2x)y=e^x ?

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

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x^2(dy)/(dx)+(x^2+2x)y=e^x

x^{2} \frac{d y}{d x} + (x^{2} + 2 x) y = e^{x}

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

Solution steps

x^{2} \frac{d y}{d x} + (x^{2} + 2 x) y = e^{x}

Solve linear ODE:

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

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

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

\frac{d}{d x} ((2 x + 5)^{\frac{1}{3}})

\int (\frac{3}{x} + 3 x) d x

\frac{d}{d x} (x (cos (x)))

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