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

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

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x^2(dy)/(dx)-2x^3e^{-1/x}=y

x^{2} \frac{d y}{d x} - 2 x^{3} e^{- \frac{1}{x}} = y

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

Solution steps

x^{2} \frac{d y}{d x} - 2 x^{3} e^{- \frac{1}{x}} = y

Solve linear ODE:

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

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

\int sin (5 x) sin (4 x) d x

(4.1) (8.2)

\frac{d}{d x} (\frac{sec ( x ) + csc ( x )}{csc ( x )})

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\frac{\partial}{\partial x} (- x^{2} y + 4)

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