(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.
Step 1 :
In this problem we have to find the integrating factor.
and also given that
Let be an integrating factor
Multiplying in equation (1)
This equation exact
Step 2 :
Step 3 :
This is the general form of the integrating factor.