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}

f (x) = 10 x^{3} - 45 x^{2} + 60 x - 30

\frac{d}{d s} (\frac{( s ^{2} - 4 s + 20 )}{s ^{2} + 6 s + 8})

y = e^{2 x}, x = 0, x = 3

\int \frac{e ^{6 t}}{t} d t

\frac{d}{d x} (e^{(\frac{- k}{x})})

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