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

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

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

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

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

Solution steps

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