MAT244-2014F > MAT244 Math--Lectures

Solving Homogenous equation: y' = f(x,y)

(1/1)

Kelly Yang:
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)/(x-y)        ---- (1)
which can be re-written 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 right-hand 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.)

Victor Ivrii:
Unless there is an initial condition there should be a constant

Kelly Yang:
Oh! I forgot to include the integration constant. Thanks!