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Diff Equation with one solution?

  1. May 12, 2010 #1
    1. The problem statement, all variables and given/known data

    Hi guys, my question is from a book on differential equation. It asks me to give a differential equation that has only a trivial solution, y = 0.

    2. Relevant equations

    3. The attempt at a solution

    I give it some thought and I can only think of a diff eq'n of y' = y, however, in this case y = e^x will also be a valid solution but not a trivial one. So I am not so sure if this is what the question wants, or there is a diff eq'n that has only one solution which is y =0. Thank you in advance.
  2. jcsd
  3. May 12, 2010 #2


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    Science Advisor
    Homework Helper

    Well, you said "y = 0", isn't that a valid answer?
    If you insist that it contains derivatives of higher order than 0, you can easily adapt it (but you need boundary conditions).
  4. May 12, 2010 #3


    Staff: Mentor

    y' = y; y(0) = 0
    This initial-value problem has only one solution.
  5. May 12, 2010 #4
    Oh ok .... that will do ... Thank you Mark44 and CompuChip.
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