What is the solution for ydx-(y-x)dy=0 ?

The solution for ydx-(y-x)dy=0 is y=x-sqrt(x^2-c_{1)},y=x+sqrt(x^2-c_{1)}

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ydx-(y-x)dy=0

y d x - (y - x) d y = 0

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

Solution steps

y d x - (y - x) d y = 0

Solve exact ODE:

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

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

y^{^{'}} + \frac{1}{2} y = 0

y^{^{''}} + 10 y^{^{'}} + y = 0

\frac{d}{d x} (ln^{2} (x + 1))

\frac{d}{d x} ((x^{2} + x)^{\frac{1}{2}})

\frac{d}{d x} ((\frac{x ^{3} - 1}{2 x ^{3} + 1})^{4})

What is the solution for ydx-(y-x)dy=0 ?
The solution for ydx-(y-x)dy=0 is y=x-sqrt(x^2-c_{1)},y=x+sqrt(x^2-c_{1)}