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

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

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

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

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

Solution steps

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

\int x^{2} - e^{- x} d x

\frac{d}{d x} (- π^{2} cos (π x))

f (x) = \frac{6 - x ^{2}}{x}

\frac{d}{d t} (2 e^{- t})

\frac{\partial}{\partial x} (y^{4} cos (5 x) \cdot 5)

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