(a) Show that if depends only on the product xy, that is,

then the equation has an integrating factor of the form µ (xy) Give the general formula for µ (xy).

(b) Use your answer to part (a) to find an implicit solution to

satisfying the initial condition y (1) = 1.

Solution :

Step 1 :

In this problem we have to find the integrating factor.

Consider

and also given that

Let be an integrating factor

Multiplying in equation (1)

This equation exact