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

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

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

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

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

Solution steps

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

Solve exact ODE:

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

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

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