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Homework Help: Solutions space (ODE)

  1. Mar 5, 2017 #1
    1. The problem statement, all variables and given/known data

    How many functions y(t) satisfy both y''+t^2*y=0 and y(0)=6?

    2. The attempt at a solution

    As this is a second order differential equation, two initial conditions (for y and y') would be needed to obtain a unique solution (cf. existence and uniqueness theorem). So the answer is 'infinitely many functions' as we are given only y(0)=6. Have I understood it correctly?
  2. jcsd
  3. Mar 5, 2017 #2


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    2017 Award

    Staff: Mentor

    As long as all those different y'(0) lead to valid solutions, that works.
  4. Mar 5, 2017 #3
    Oh, OK. Many thanks. :)
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