What is the solution for x^2ydy-xy^2dx-x^3y^2dx=0 ?

The solution for x^2ydy-xy^2dx-x^3y^2dx=0 is y=(c_{1}x}{e^{\frac{-x^2+2c_{1})/2}}

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x^2ydy-xy^2dx-x^3y^2dx=0

x^{2} y d y - x y^{2} d x - x^{3} y^{2} d x = 0

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

Solution steps

x^{2} y d y - x y^{2} d x - x^{3} y^{2} d x = 0

Solve linear ODE:

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

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

What is the solution for x^2ydy-xy^2dx-x^3y^2dx=0 ?
The solution for x^2ydy-xy^2dx-x^3y^2dx=0 is y=(c_{1}x}{e^{\frac{-x^2+2c_{1})/2}}