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

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

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

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

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

Solution steps

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

Solve Bernoulli ODE:

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

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

\int - \frac{5}{12 - 12 x ^{2}} d x

\frac{d}{d x} (\frac{x ^{2} + 5}{x ^{2} + 6 x})

y = x^{2} - 2 x - 3, (2, - 3)

n = 0 \sum \infty c n (x - 8)^{n}

\frac{\frac{s}{2} + \frac{5}{3}}{s ^{2} + 4 s + 6}

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