The problem is solve : xp + yq =z
I have done the problem in this way :
the auxiliary equation is dx/x = dy/y = dz/z
Taking the first two term, it can be written as
dx/x = dy/y
Integrating,
ln x = ln y + ln a (ln a = constant)
or, x/y = a
Taking the last two terms, it can be written as,
dy/y = dz/z
Integrating,
ln y = ln z + ln b (ln b = constant)
or, y/z = b
therefore, the solution is f [ x/y, y/z ] = 0
Please tell whether the above solution is correct or not. I will be very thankful.