Question

Find the general solution of the following differential equation: 

cos x(1 + cos y)dx – sin y(1 + sin x)dy = 0

Answer 1

Rearranging the terms we get:

\(\frac{cosx\,dx}{(1+sinx)}\) = \(\frac{cosy\,dy}{(1+siny)}\)

Integrating both the sides we get:

⇒ \(\int\frac{cosx\,dx}{(1+sinx)}\) = \(\int\frac{cosy\,dy}{(1+siny)}\) + c

⇒ log|1 + sin x| = - log|1 + cos y| + log c 

⇒ log|1 + sin x| + log|1 + cos y| = log c 

⇒ (1 + sin x)(1 + cos y) = c 

Ans: (1 + sin x)(1 + cos y) = c