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Differential Equation problem

  1. Sep 5, 2015 #1
    Solve the given differential equation by separation of variables.

    (dy/dx)= (xy+3x-y-3)/(xy-2x+4y-8)

    First, I noticed when i divided both sides by the left hand side and multiplied both sides by dx, nothing cancelled or seemed to work.

    I got to thinking.

    on the right hand side I preformed long division.

    i divided xy+3x-y-3 by xy-2x+4y-8.

    I get 1 + (5x-5y+5)/(xy-2x+4y-8)

    (dy/dx)= 1 + (5x-5y+5)/(xy-2x+4y-8)

    I am stuck here. Any help is welcomed and appreciated.
     
  2. jcsd
  3. Sep 5, 2015 #2
    I think a better approach is beginning instead by factoring the RHS. From there it should be clear how to solve via separation of variables.
     
  4. Sep 5, 2015 #3
    wow, i over thought this problem. thanks a lot.

    factoring the left hand side.

    (y+3)(x-1)/(y-2)(x+4)

    Left hand side= (y-2)/(y+3)dy

    right hand side=(x-1)/(x+4)dx

    then I integrate. the process is kind of lengthy, requiring trivial integration.

    the answer is (x+4)^5=c(e^x)(e^-y)(y+3)^5.

    I can't take you enough.
     
  5. Sep 7, 2015 #4
    That looks like a correct implicit soln; you can also tidy up the RHS of your answer a little by applying some rules of exponents:
    \begin{equation} e^{x}e^{-y} = e^{x-y} \end{equation}
     
  6. Sep 7, 2015 #5
    yes, you are correct. thanks a lot.

    Do you recommended a an intro ode book?

    we are using zill in our class, and it is a bit to chatty. The graphics make the layout of the book a little hard to read in my opinion and he is too loose ( doesn't really use mathematical language) in his explanations.
     
  7. Sep 7, 2015 #6
    I wouldn't be able to help you there. I also used a text co-authored by Zill when I took differential ('Differential Equations with Boundary-Value Problems' by Zill and Cullen 7ed.) when I took differential.
    I saw a text by Ross recommended in the thread "How to self-study mathematics?" However, I haven't ever had the opportunity to see what it's like myself.
     
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