⇒ \(\frac{dy}{dx}\) = \(\frac{y}{x-\sqrt{xy}}\)
= \(\frac{1}{\frac{x}{y}-\sqrt{\frac{x}{y}}}\)
= \(\frac{1}{(\frac{x}{y})^{-1}-\sqrt({\frac{x}{y})^{-1}}}\)
⇒ \(\frac{dy}{dx}\) = \(f(\frac{y}{x})\)
⇒ the given differential equation is a homogenous equation.
The solution of the given differential equation is :
Put y = vx
Integrating both the sides we get:
Resubstituting the value of y = vx we get