x dx + y dy \(=\frac{x\,dx+y\,dy}{x^2+y^2}\)
⇒ 2x dx + 2y dy \(=\frac{2x\,dx+2y\,dy}{x^2+y^2}\) (Multiply both sides by 2)
⇒ ∫2x dx + ∫2y dy \(=\int\frac{2x\,dx+2y\,dy}{x^2+y^2}\)
⇒ x2 + y2 = ln(x2 + y2) + c (∵ d[ln(x2+y2)] \(=\frac{2x\,dx+2y\,dy}{x^2+y^2})\)