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

The solution for (dy)/(dx)=(x-y)/(x+y) 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)/(x+y)

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

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}{x + y}

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