Given, the differential equation is

(1)

We have to solve the equation by separation of variables.

We can rewrite the above equation as

(2)

We know, and

(3)

To solve this differential equation, we can separate the variables by putting all the y terms on one side and all the x terms on the other side:

(4)

Now we can integrate both sides with respect to their respective variables:

(5)

We know that,

We can rewrite the above equation as

(6)

Now we can integrate both sides with respect to their respective variables:

On the left side, we get;

(7)

On the right side, we get;

(8)

We can simplify this expression as

(9)

By multiplying , we get this expression as

(10)

Hence we can Solve cosec(y)dx+sec^2(x)dy=0 by separable method easily.