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}

y = 2, y = x^{2} + 1

\frac{d}{d x} ((lo g_{2} (x))^{4})

\frac{d}{d x} (x^{2} - 7 x + 7)

y^{^{''}} + 3 y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 1

3 x^{\frac{3}{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