The equation of the curve passing through the point (1, 1) and whose slope is $\frac{2ay}{x(y-a)}$, is:

$y^a.x^{2a}=e^{y-1}$

$\frac{dy}{dx}=\frac{2ay}{x(y-a)}⇒\int\frac{dx}{x}=\int\frac{(y-a)dy}{2ay}$

$⇒\log x=\frac{1}{2a}[y-a\log y]+c⇒x\sqrt{y}=k.e^{y/2a}$

As curve passes through (1, 1) $⇒k=e^{-1/2a}$

$⇒x\sqrt{y}=e^{\frac{(y-1)}{2a}}⇒x^{2a}y^a=e^{y-1}$