y = px + \(x\sqrt{1+p^2}\Rightarrow y\) \(=(p+\sqrt{1+p^2})x\;\;...(1)\)
\(\frac{dy}{dx}=p+\sqrt{1+p^2}\)
Put \(p+\sqrt{1+p^2}=\frac{dy}{dx}\) in equation (1), we get y \(=\frac{dy}{dx}x\)
\(\Rightarrow\frac{dy}{dx}=\frac{y}{x}\) which is differential equation for given curve.