Question

The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is ______.

Options

• `sinx/siny` = c

• sinx siny = c

• sinx + siny = c

• cosx cosy = c

Answer 1

The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is sinx siny = c.

Explanation:

The given differential equation is cosx siny dx + sinx cosy dy = 0

⇒ sinx cosy dy = – cosx siny dx

⇒ `cosy/siny "d"y = - cosx/sinx "d"x`

⇒ coty dy = – cotx dx

Integrating both sides, we have

⇒ `int coty  "d"y = - int cot x  "d"x`

⇒ `log|sin y| = - log|sin| + log"c"`

⇒ `log|siny| + log|sinx| = log"c"`

⇒ `log|siny . sin x| = log"c"`

⇒ sinx siny = c