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

Given Differential Equation :

Formula :

i)

ii)

iii)

iv)

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

………eq(1)

Equation (1) is of the form

Where, and

Therefore, integrating factor is

………

………

General solution is

………eq(2)

Let,

Let, u=sin 2x & v=sin x

………

………

Again let, u=cos 2x & v=cos x

………

………

Substituting I in eq(2),

Therefore, general solution is