What is the solution for (2y^2x+3x^2)dx+2x^2ydy=0 ?

The solution for (2y^2x+3x^2)dx+2x^2ydy=0 is y=(sqrt(-x^3+c_{1)})/x ,y=-(sqrt(-x^3+c_{1)})/x

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(2y^2x+3x^2)dx+2x^2ydy=0

(2 y^{2} x + 3 x^{2}) d x + 2 x^{2} y d y = 0

y = \frac{- x ^{3} + c _{1}}{x}, y = - \frac{- x ^{3} + c _{1}}{x}

Solution steps

(2 y^{2} x + 3 x^{2}) d x + 2 x^{2} y d y = 0

Solve exact ODE:

y = \frac{- x ^{3} + c _{1}}{x}, y = - \frac{- x ^{3} + c _{1}}{x}

y = \frac{- x ^{3} + c _{1}}{x}, y = - \frac{- x ^{3} + c _{1}}{x}

\frac{d}{d x} (\frac{x ^{3}}{x + 2})

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\frac{d}{d x} ((1 + 2 x)^{\frac{1}{2}})

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