Use implicit differentiation to confirm that the equation defines implicit solutions of the differential equation.

Question

ln y = xc + C; dy/dx = (y^2)/(1-xy)

Answer 1

I assume that you mean ln(y) = xy + C then differeniate to get

(1/y)y' = y + xy' multiply through by y to get y' = y^2 + xyy' factor out y' to get

y'(1-xy) = y^2 Then y' = y^2/(1-xy)