Let \(y=y(x)\) be the solution of the differential equation \(\mathrm{xtan}\left(\frac{\mathrm{y}}{\mathrm{x}}\right)\ma…

Let \(y=y(x)\) be the solution of the differential equation \(\mathrm{xtan}\left(\frac{\mathrm{y}}{\mathrm{x}}\right)\mathrm{dy}=\left(\mathrm{ytan}\left(\frac{\mathrm{y}}{\mathrm{x}}\right)-\mathrm{x}\right)\mathrm{dx},-1\leq \mathrm{x}\leq 1,\mathrm{y}\left(\frac{1}{2}\right)=\frac{\pi }{6}\) Then the area of the region bounded by the curves \(x=0,x=\frac{1}{\sqrt{2}}\) and \(y=y(x)\) in the upper half plane is: