What is the solution for 2y(y-1)dx+x(2y-1)dy=0 ?

The solution for 2y(y-1)dx+x(2y-1)dy=0 is y=(x+sqrt(x^2+c_{1)})/(2x),y=(x-sqrt(x^2+c_{1)})/(2x)

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2y(y-1)dx+x(2y-1)dy=0

2 y (y - 1) d x + x (2 y - 1) d y = 0

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

Solution steps

2 y (y - 1) d x + x (2 y - 1) d y = 0

Solve separable ODE:

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

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

\frac{d y}{d x} + \frac{1}{50} y = 4

4 x \frac{d y}{d x} + 7 y = 0

\frac{d v}{d t} = 32.2 - 0.8 v

y^{^{'}} = \frac{- t}{y}

\frac{d y}{d x} = 3 e^{x - y}, y (0) = ln (8)

What is the solution for 2y(y-1)dx+x(2y-1)dy=0 ?
The solution for 2y(y-1)dx+x(2y-1)dy=0 is y=(x+sqrt(x^2+c_{1)})/(2x),y=(x-sqrt(x^2+c_{1)})/(2x)