Solve the following differential equation :

OR

Solve the following differential equation :

We have given

We can write it as,

Now, The equation is in the form of a linear differential equation as

When we compare the equation with the linear equation , we get

Let x² - 1 = t then 2xdx = dt

When substituting the value of t , we get

I.F = x² - 1 + C

Now, The general solution for a linear equation is

Hence, This the required solution of given differential equation.

OR

Re - writing the equation as

Now separating variable x on one side and variable y on another side, we have

Multiplying and dividing the numerator of LHS by x

Assuming 1+y² = t² and 1+x² = v²

Differentiating we get,

ydy = tdt

xdx = vdv

Substituting these values in above differential equation

Integrating both sides

Adding 1 and subtracting 1 to the numerator of RHS

We know that,

Therefore,

Substituting t and v in above equation