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

The solution for (dy)/(dx)=(x+y)/(y-x) is y=(2x+sqrt(8x^2+c_{1)})/2 ,y=(2x-sqrt(8x^2+c_{1)})/2

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(dy)/(dx)=(x+y)/(y-x)

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

y = \frac{2 x + 8 x ^{2} + c _{1}}{2}, y = \frac{2 x - 8 x ^{2} + c _{1}}{2}

Solution steps

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

Solve exact ODE:

y = \frac{2 x + 8 x ^{2} + c _{1}}{2}, y = \frac{2 x - 8 x ^{2} + c _{1}}{2}

y = \frac{2 x + 8 x ^{2} + c _{1}}{2}, y = \frac{2 x - 8 x ^{2} + c _{1}}{2}

What is the solution for (dy)/(dx)=(x+y)/(y-x) ?
The solution for (dy)/(dx)=(x+y)/(y-x) is y=(2x+sqrt(8x^2+c_{1)})/2 ,y=(2x-sqrt(8x^2+c_{1)})/2