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1st order ivp

  1. Mar 7, 2012 #1
    y' = x
    x' = -5y-4x

    y(0) = 1
    x(0) = 0

    after finding the general solution as shown here
    http://www.wolframalpha.com/input/?i=y'+=+x,+x'+=+-5y-4x

    how do you go about applying the initial values and finding the complete solution?
     
  2. jcsd
  3. Mar 7, 2012 #2

    HallsofIvy

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    Your general solution should have two undetermined coefficients. Substitute 0 for t, set x= 0, y= 1 and you will have two equations to solve for the two coefficients.
     
  4. Mar 7, 2012 #3
    actually I don't think wolfram alpha has done the correct thing in making x and y a function of t as there's no mention of another variable in the original equations. What would you do when they aren't functions of t?
     
  5. Mar 8, 2012 #4

    HallsofIvy

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    You can call the independent variable whatever you want! What did you mean by x' and y'? I assumed the primes were derivatives. With respect to what variable?
     
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