What is the solution for x^2(dy)/(dx)=xy+3y^2 ?

The solution for x^2(dy)/(dx)=xy+3y^2 is y= x/(-3ln(x)+c_{1)}

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x^2(dy)/(dx)=xy+3y^2

x^{2} \frac{d y}{d x} = x y + 3 y^{2}

y = \frac{x}{- 3 ln ( x ) + c _{1}}

Solution steps

x^{2} \frac{d y}{d x} = x y + 3 y^{2}

Solve Bernoulli ODE:

y = \frac{x}{- 3 ln ( x ) + c _{1}}

y = \frac{x}{- 3 ln ( x ) + c _{1}}

50 x^{2} e^{- x} + 8

\frac{d}{d u} (\frac{u}{v})

y y^{^{'}} = x (y^{2} + 1)

\frac{d}{d x} (\frac{x e ^{x} - e ^{x}}{x ^{2}})

x \to 0 lim (3 x + 1)

What is the solution for x^2(dy)/(dx)=xy+3y^2 ?
The solution for x^2(dy)/(dx)=xy+3y^2 is y= x/(-3ln(x)+c_{1)}