What is the solution for (xy-1)dx+(x^2-xy)dy=0 ?

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

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(xy-1)dx+(x^2-xy)dy=0

(x y - 1) d x + (x^{2} - x y) d y = 0

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

Solution steps

(x y - 1) d x + (x^{2} - x y) d y = 0

Solve exact ODE:

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

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

\frac{d y}{d x} = y (10 - y)

\frac{d}{d x} (8 sin (x) - 8 x cos (x))

f (4) = 4 x^{\frac{5}{4}} + 4 x^{\frac{3}{2}} + 5 x

ln (9 x)

f (x) = x - 1, (5, 2)

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