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}

\frac{d}{d x} (4 + \frac{4}{x})

\int \frac{x ^{4} + 3 x ^{2} + 5}{x ^{4}} d x

\frac{d x}{d t} = 8 + 4 sin (\frac{t}{4}) - \frac{x}{100}, x (0) = 70

f (x) = \frac{x}{2 x - 8}, at x = 3

x \to \infty lim (\frac{5}{x} - 4)

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