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

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

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

x^{2} y^{^{'}} - 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} y^{'} (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}}}

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f (x) = \frac{3}{x ^{3}}

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