Answer :

Given equation:

On-rearranging the term, we get,

Now, this is a homogenous differential equation of order 1.

Let y = vx and

Therefore,

Integrating both sides, we get,

Now, we know that,

and

Therefore,

Putting the value of y, we get,

At x = 1, y = 0,

C = 1

Hence,

OR

Given Equation:

Dividing the whole equation by (1 + x^{2}), we get,

Now, this is a linear equation of the form,

We know that the solution of this equation is given by,

Where

Therefore, for a given equation,

Let 1 + x^{2} = t

Differentiating both sides, we get,

2x dx = dt

Therefore,

The solution of the equation:

At x = 0, y = 0

Therefore,

0(1 + 0) = 0 + c

c = 0

Hence,

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