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


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


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.