I am unable to solve this question sirs,
$$\frac{dy}{dx} = \dfrac{-x\sqrt{1+x^2}}{y\sqrt{1+y^2}}$$
no way futher Please help.
This equation is separable. Rewrite as $$y\sqrt{1+y^2}\,dy=-x\sqrt{1+x^2}\,dx,$$ integrate both sides, and solve for $y$. Don't forget that you'll need a constant of integration on one side.