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Solving for a Differential Equation with Inspection.

  1. Mar 21, 2012 #1
    I'm rather bad at solving by inspection, and right now I am stuck on a problem I can't solve.


    1.http://www.texify.com/img/%5CLARGE%5C%21y%28x%5E2y%5E2-m%29dx%2Bx%28x%5E2y%5E2%2Bn%29dy%3D0.gif [Broken]



    2.The attempt at a solution
    http://www.texify.com/img/%5CLARGE%5C%21x%5E2y%5E3dx-mdx%2Bx%5E3y%5E2dy%2Bndy%3D0.gif [Broken]

    Rearrange and divide by x^2 * y^2

    http://www.texify.com/img/%5CLARGE%5C%21ydx%2Bxdy%20%3D%20%28mydx-nxdy%29/x%5E2y%5E2.gif [Broken]

    I know that xdy+ydx = d(xy) buy I don't know what to do with the other side. If I try to make the right side into d(mx/ny) I'm left over with an x^2 that I don't know how to get rid of.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Mar 21, 2012 #2

    tiny-tim

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    Welcome to PF!

    Hi Kiziaru! Welcome to PF! :smile:

    (I haven't actually tried to solve this :redface:, but …)

    my immediate reaction on seeing that m and n was to think "xm and yn"
     
  4. Mar 21, 2012 #3
    Re: Welcome to PF!

    Thanks! I've always lurked on this site, but I never posted because most of what I needed help with was already answered, until today. :frown:

    Also, I hate to sound dumb, but what wizardry is this? How can I make m and n into exponents? And is this part of a plan to get d(arctan(y/x))?
     
  5. Mar 21, 2012 #4

    tiny-tim

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    no specific plan … just a vague idea :smile:

    remember, you can multiply the whole equation by anything you like :wink:
     
  6. Mar 21, 2012 #5

    LCKurtz

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    What I see is that if you ignore the terms with m and n, the other part is exact...
     
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