1st order ivp

  • Thread starter Ry122
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  • #1
565
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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?
 

Answers and Replies

  • #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.
 
  • #3
565
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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?
 
  • #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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