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MAT244-2014F => MAT244 Math--Lectures => Topic started by: Kelly Yang on December 02, 2014, 01:48:36 PM

Title: Solving Homogenous equation: y' = f(x,y)
Post 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)/(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.)
Title: Re: Solving Homogenous equation: y' = f(x,y)
Post by: Victor Ivrii on December 02, 2014, 01:56:12 PM
Unless there is an initial condition there should be a constant
Title: Re: Solving Homogenous equation: y' = f(x,y)
Post by: Kelly Yang on December 02, 2014, 01:59:37 PM
Oh! I forgot to include the integration constant. Thanks!