The solution of the differential equation : \(\frac{dx}{x} + \frac{dy}{y}\) = 0 is :

\(\frac{1}{x} + \frac{1}{y}\) = c xy = C x + y = c log x . log y = c

xy = C

\(\frac{dx}{x} + \frac{dy}{y}\) = 0 \(\frac{dx}{x} =- \frac{dy}{y}\)  log x = - log y + log C xy = C