Sol. We have,

x + y = y 2 log x

+ y = y 2 This is in the form of Bernoulli's differential equation. Dividing both sides by y

2 , we get

+ =

Let = v. Then,

– =

Substituting these in the given differential equation, we get

⇒ – + v = ⇒ + v = – ... (i)

This is a linear differential equation of the form

+Pv = Q, where

P = – and Q = –

We have,

I.F. = = = e –log x = = x –1 =

Multiplying both sides of (i) by , we get

+ v =

Integrating both sides with respect to x, we get

v = dx+C

[Using: v (I.F.) = ]

⇒ v. = –

⇒ v. = –

⇒ v. = –

⇒ v. = –

⇒ v. = + C

⇒ = + C

[Putting v = 1/y]

This is the required solution of the given differential equation.