Answer :

**Given,** We have a differential equation,

**To Find:** Prove that it is a homogenous differential equation and solve.

**Explanation:** We have

It can be written as

Now, to prove that it is a Homogenous differential equation, we put x = λx and y = λy then

Now, Taking λ as common from both numerator and denominator, we get

If, then it is an homogenous differential equation

Now, Solution of this differential equation is

Put y = v x

Then,

So, When we compare this derivative from the given equation we get

Taking x as common from R.H.S

On integrating both sides,

For Solving L.H.S

Put v^{2} + v + 1 = t

2v + 1 dv = dt

So,

Now, Put the value of v = y/ x, we get

**Hence, This is the solution of Given differential equation.**

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