Find the general solution for each of the following differential equations.

Given Differential Equation :

Formula :

v)

vi)

vii)

viii) General solution :

For the differential equation in the form of

General solution is given by,

Where, integrating factor,

Answer :

Given differential equation is

Dividing above equation by sin x,

………eq(1)

Equation (1) is of the form

Where, and

Therefore, integrating factor is

………

= sin x ………

General solution is

………eq(2)

Let,

Put sin x=t => cos x.dx=dt

………

Substituting I in eq(2),

Therefore, general solution is