What is the solution for 2xy+(dy)/(dx)=(6x)/(y^2) ?

The solution for 2xy+(dy)/(dx)=(6x)/(y^2) is y=\sqrt[3]{-e^{-3x^2-c_{1}}+3}

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2xy+(dy)/(dx)=(6x)/(y^2)

2 x y + \frac{d y}{d x} = \frac{6 x}{y ^{2}}

y = 3 - e^{- 3 x^{2} - c_{1}} + 3

Solution steps

2 x y + \frac{d y}{d x} = \frac{6 x}{y ^{2}}

Solve separable ODE:

y = 3 - e^{- 3 x^{2} - c_{1}} + 3

y = 3 - e^{- 3 x^{2} - c_{1}} + 3

(2 x y - y - 4 x + 2) d x + d y = 0

\frac{1 + cos ( 2 x )}{1 + sin ( y )} + y^{^{'}} = 0

e^{- x} sin (y) \frac{d y}{d x} = 1 + e^{- x}

\frac{df}{d x} = 2 f (x) tan (x)

\frac{d y}{d x} - x y = 3 x

What is the solution for 2xy+(dy)/(dx)=(6x)/(y^2) ?
The solution for 2xy+(dy)/(dx)=(6x)/(y^2) is y=\sqrt[3]{-e^{-3x^2-c_{1}}+3}