What is the solution for y^2dx=(2xy+x^2)dy ?

The solution for y^2dx=(2xy+x^2)dy is y=(-x+sqrt(x^2+4c_{1)x})/2 ,y=(-x-sqrt(x^2+4c_{1)x})/2

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y^2dx=(2xy+x^2)dy

y^{2} d x = (2 x y + x^{2}) d y

y = \frac{- x + x ^{2} + 4 c _{1} x}{2}, y = \frac{- x - x ^{2} + 4 c _{1} x}{2}

Solution steps

y^{2} d x = (2 x y + x^{2}) d y

Solve using substitution:

y = \frac{- x + x ^{2} + 4 c _{1} x}{2}, y = \frac{- x - x ^{2} + 4 c _{1} x}{2}

y = \frac{- x + x ^{2} + 4 c _{1} x}{2}, y = \frac{- x - x ^{2} + 4 c _{1} x}{2}

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What is the solution for y^2dx=(2xy+x^2)dy ?
The solution for y^2dx=(2xy+x^2)dy is y=(-x+sqrt(x^2+4c_{1)x})/2 ,y=(-x-sqrt(x^2+4c_{1)x})/2