1.The general solution of 1+x2+y2+x2y2+xydydx=0\sqrt{1 + x^2 + y^2 + x^2y^2} + xy\frac{dy}{dx} = 01+x2+y2+x2y2+xydxdy=0 (where CCC is a constant of integration)a.1+y2+1+x2=12loge(1+x2−11+x2+1)+C\sqrt{1+y^2} + \sqrt{1+x^2} = \frac{1}{2}\log_e\left(\frac{\sqrt{1+x^2}-1}{\sqrt{1+x^2}+1}\right) + C1+y2+1+x2=21loge(1+x2+11+x2−1)+Cb.1+y2−1+x2=12loge(1+x2−11+x2+1)+C\sqrt{1+y^2} - \sqrt{1+x^2} = \frac{1}{2}\log_e\left(\frac{\sqrt{1+x^2}-1}{\sqrt{1+x^2}+1}\right) + C1+y2−1+x2=21loge(1+x2+11+x2−1)+Cc.1+y2+1+x2=12loge(1+x2+11+x2−1)+C\sqrt{1+y^2} + \sqrt{1+x^2} = \frac{1}{2}\log_e\left(\frac{\sqrt{1+x^2}+1}{\sqrt{1+x^2}-1}\right) + C1+y2+1+x2=21loge(1+x2−11+x2+1)+Cd.1+y2−1+x2=12loge(1+x2+11+x2−1)+C\sqrt{1+y^2} - \sqrt{1+x^2} = \frac{1}{2}\log_e\left(\frac{\sqrt{1+x^2}+1}{\sqrt{1+x^2}-1}\right) + C1+y2−1+x2=21loge(1+x2−11+x2+1)+CLogin to continueOnly logged in users canattempt or see the solution.
