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

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

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1/x (dy)/(dx)-2/(x^2)y=x^2e^{-x}

\frac{1}{x} \frac{d y}{d x} - \frac{2}{x ^{2}} y = x^{2} e^{- x}

y = - e^{- x} x^{3} - e^{- x} x^{2} + c_{1} x^{2}

Solution steps

\frac{1}{x} \frac{d y}{d x} - \frac{2}{x ^{2}} y = x^{2} e^{- x}

Solve linear ODE:

y = - e^{- x} x^{3} - e^{- x} x^{2} + c_{1} x^{2}

y = - e^{- x} x^{3} - e^{- x} x^{2} + c_{1} x^{2}

\frac{5}{x ^{5}} + \frac{3}{x ^{2}}

\int \frac{y - y}{y ^{2}} d y

\int (ln (x))^{2} d x

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

\frac{\partial}{\partial y} ((x + y)^{2} + (x + 1)^{2})

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