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}

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)}