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

Given Differential Equation :

Formula :

i)

ii)

iii)

iv) 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 (1 – x²),

………eq(1)

Equation (1) is of the form

Where, and

Therefore, integrating factor is

Let (1 – x²) = f(x)

Therefore f’(x) = -2x

………

………

General solution is

……eq(2)

Let

Put (1 – x²) = t

Substituting I in eq(2)

Multiplying above equation by ,