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

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

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

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

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

Solution steps

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

Solve Bernoulli ODE:

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

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

\int (sin (2 x) + cos (2 x)) d x

y = x^{2}, y = 2 x - x^{2}

\frac{d}{d x} (\frac{q x + r ( q , x , t )}{s x + t})

\int (x + 4) 6 - x d x

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