Author Topic: Solving Homogenous equation: y' = f(x,y)  (Read 489 times)

Kelly Yang

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Solving Homogenous equation: y' = f(x,y)
« 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)/(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.)
« Last Edit: December 02, 2014, 02:45:04 PM by Kelly Yang »

Victor Ivrii

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Re: Solving Homogenous equation: y' = f(x,y)
« Reply #1 on: December 02, 2014, 01:56:12 PM »
Unless there is an initial condition there should be a constant

Kelly Yang

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Re: Solving Homogenous equation: y' = f(x,y)
« Reply #2 on: December 02, 2014, 01:59:37 PM »
Oh! I forgot to include the integration constant. Thanks!