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

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

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

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

y = - \frac{2 e ^{2 c_{1}} x ^{2}}{1 - e ^{2 c_{1}} x ^{2}}

Solution steps

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

Solve separable ODE:

y = - \frac{2 e ^{2 c_{1}} x ^{2}}{1 - e ^{2 c_{1}} x ^{2}}

y = - \frac{2 e ^{2 c_{1}} x ^{2}}{1 - e ^{2 c_{1}} x ^{2}}

\frac{\partial}{\partial y} (\frac{x y}{x + y})

f (t) = \frac{3}{t}

\frac{d}{d x} (- \frac{3}{4} e^{- \frac{x}{4}})

\frac{\partial}{\partial x} (- e^{- x} cos (y))

\int \frac{4 x ^{5}}{9 - 16 x ^{6}} d x

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