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Second order DE

  1. Jun 20, 2005 #1
    Hello, not sure if it's a typo in the book but I can't work this out:

    y'' + y(x^2 + e^x) = 0;

    It's second order but both dependent and independent variables are present, and i am stuck.
    You don't have to solve it for me entirely, a hint would be great.

    Thanks in advance.
  2. jcsd
  3. Jun 20, 2005 #2


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    The coeff are not constant and one is a polynomial and the other a transcendental function.I doubt one can find an analytical method to find the 2 solutions.

  4. Jun 20, 2005 #3
    Are you saying that there's a typo in the problem?
    (it's a first Diff Eq course)
  5. Jun 20, 2005 #4


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    Not necessarily. Many first course d.e. texts introduce "series solutions" but that's the only way I see to do this.
  6. Jun 20, 2005 #5


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    When in doubt guess. I ain't proud. I used NDSolve with initial conditions (just out of thin air) of y(0)=1,y'(0)=0. The results are below. I know it's not a solution but at least it's the start of a handle. :smile:

    Edit: Wait a minute. That IS a solution. I mean it's not an analytically derived one. :smile:

    Attached Files:

    Last edited: Jun 20, 2005
  7. Jun 20, 2005 #6
    I'm sure it's somehow deducible with series, but unfortunately the book does not discuss that anywhere, i guess i'll have to google. I wish the book or the instructor would give more of "and why do we do this?" rather than "here's how: plug and chug".

    Thanks everyone.
    Last edited: Jun 20, 2005
  8. Jul 27, 2005 #7
    You should use series method to solve this diff eq.
    It's hard to explain the method in this tiny box(!). I suggest to check out an elemantary diff eq book and read the chapter about the series method.
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