1st order ivp

  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. HallsofIvy

    HallsofIvy 40,678
    Staff Emeritus
    Science Advisor

    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. 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. HallsofIvy

    HallsofIvy 40,678
    Staff Emeritus
    Science Advisor

    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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