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Coupled ODE's

  1. Mar 12, 2009 #1
    1. The problem statement, all variables and given/known data
    I am having trouble remembering how to uncouple these.



    2. Relevant equations
    [tex] \frac{dt}{ds}=1[/tex]
    [tex] \frac{du}{ds}=2tu[/tex]



    3. The attempt at a solution
    I remember putting it into a matrix.
    [tex] x'=\lambda x [/tex]
     
  2. jcsd
  3. Mar 12, 2009 #2

    Mark44

    Staff: Mentor

    The equation with du/ds is nonlinear, so this system might not be amenable to uncoupling by matrix methods, which involves finding eigenvalues and eigenvectors, and using them to diagonalize a matrix.

    Alternatively, I think it works to solve for t as a function of s in the first equation, and substitute for t in the second equation, and solve it for u.

    To get you started, if dt/ds = 1, what is t as a function of s? Hint: there is not just one solution.
     
  4. Mar 12, 2009 #3
    t(s)=s+C

    Plugging that into the latter u = A Exp(s^2+Cs). Is that right?
     
  5. Mar 12, 2009 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Check it your self! Certainly dt/ds= 1. What is du/ds? Is it equal to 2tu?
     
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