Solve the following differential equation:

OR

Solve the following differential equation:

Given: Differential equation:

To find: solution of the differential equation

Formula used:

This is a linear differential equation:

which is solved by

Solution is,

Therefore,

Solution is,

OR

To find: solution of the differential equation:

Integrating both sides:

Using Partial function:

On comparing:

A + B = 2, B + C = 1 and A + C = 0

A + C = 0

⇒ C = -A

B + C = 1

⇒ B – A = 1

⇒ B = 1 + A

A + B = 2

⇒ A + 1 + A = 2

⇒ 2A = 1

So,

Now,

Let x² + 1 = t

⇒ 2x dx = dt

Put t = x² + 1:

Hence, the solution is