Toronto Math Forum
MAT2442014F => MAT244 MathLectures => Topic started by: Kelly Yang on December 02, 2014, 01:48:36 PM

How do you solve homogeneous equations:
y' = f(x,y) , where f is a function of x/y??
For example, given the equation:
y' = (y)/(xy)  (1)
which can be rewritten as:
y' = (1)/((x/y)  1)  (2)
My attempt at the solution was to set u = x/y, and I found y' in terms of u and x, which I then equated to the righthand side of (2). After simplifying and integrating, my final answer is:
x/y = ln(1/y) + c
I was wondering if it's okay to leave this as the final solution to the question.
(This question was given as an example in yesterday's Day class, I'm not sure if this was a textbook question.)

Unless there is an initial condition there should be a constant

Oh! I forgot to include the integration constant. Thanks!