From the first two, x'-y'=x^2-y^2=(x-y)(x+y) and using the third, x'-y'=(x-y)(u'/u)... Integrate by separating variables after that.
I'm trying to understand a solved problem in our notes and can't find a similar technique used elsewhere, so I'm asking for some assistance in understanding what exactly they did.
The problem:
Find a general solution to the equation
and the particular solution when
Solution:
The characteristic equations are:
I don't really understand these next steps they do which is:
These imply that for some constant
and
from which it follows that two integrals are for constants ( )
or
There are a few more steps after this, but I guess I'll ask about those if I don't understand them after I understand these steps.
Thanks for any assistance.