Let the solution curve y=y(x) of the differential equation [x/(√(x^2-y^2))+e^(y/x)] x (d y)/(d x)=x+[x/(√(x^2-y^2))+e^(y/x)] y pass through the…

Let the solution curve $\displaystyle y=y(x)$ of the differential equation $$\left[\frac{x}{\sqrt{x^2-y^2}}+e^{\frac{y}{x}}\right] x \frac{d y}{d x}=x+\left[\frac{x}{\sqrt{x^2-y^2}}+e^{\frac{y}{x}}\right] y $$ pass through the points $\displaystyle (1,0)$ and $\displaystyle (2 \alpha, \alpha), \alpha>0$. Then $\displaystyle \alpha$ is equal to