Question

Solve the differential equation: 

cosec³x dy - cosec y dx = 0.

Answer 1

Cosec³ x dy - cosec y dx = 0

⇒ sin y dy = sin³ x dx

Integrating both sides,

⇒ \(\int \,sin\,y\,dy=\frac{1}{4}\int\,[3\,sin\,x-sin\,3x]dx+c\)

⇒ \(-cos\,y=\frac{1}{4}\left[-3\,cos\,x+\frac{cos\,3x}{3}\right]+c\)

⇒ \(\frac{3}{4}\,cos\,x-\frac{cos\,3x}{12}-cos\,y+c=0\)