Let C_1 be the curve obtained by the solution of differential equation 2 x y (d y)/(d x)=y^2-x^2, x>0. Let the curve C_2 be the solution of (2 x…

Let $\displaystyle \mathrm{C}_1$ be the curve obtained by the solution of differential equation $\displaystyle 2 x y \frac{\mathrm{~d} y}{\mathrm{~d} x}=y^2-x^2, x>0$. Let the curve $\displaystyle \mathrm{C}_2$ be the solution of $\displaystyle \frac{2 x y}{x^2-y^2}=\frac{\mathrm{d} y}{\mathrm{~d} x}$. If both the curves pass through $\displaystyle (1,1)$, then the area enclosed by the curves $\displaystyle \mathrm{C}_1$ and $\displaystyle \mathrm{C}_2$ is equal to :