Evaluate the differential equation

Question

Y=px+x√(1+p^2)

Answer 1

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.