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}}}

\int \frac{2 x}{1 + 2 x ^{2}} d x

f (x) = (5 x - 1)^{4}, at x = 2

\frac{\partial}{\partial x} (x^{2} \cdot e^{x})

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

\int \frac{1}{x ^{2}} 2 - \frac{1}{x} d x

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}}