Solve the differential equation cosec y dx + sec 2x dy = 0 by separation of variables.

Solution: 

Given: Differential equation is cosec y dx + sec 2x dy = 0 --- (1)

By variable separable method of differential equation the given differential equation must be of the form

f(x).dx = g(y).dy or

f(x) dx ± g(y) dy = 0

Divide equation(1) by (cosec y.sec 2x)

(1/sec 2x) dx + (1/cosec y) dy = 0

cos 2x dx + sin y dy = 0

Integrating

∫cos 2x dx + ∫sin y dy = C

(sin 2x / 2) - cos y = C

Where, C is an arbitrary constant.

Solve the differential equation cosec y dx + sec 2x dy = 0 by separation of variables.

Summary:

Solution of the differential equation cosec y dx + sec 2x dy = 0 by separable variables is (sin 2x / 2) - cos y = C.