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Find the general solution of a differential equation

  1. Feb 7, 2012 #1
    1. The problem statement, all variables and given/known data

    I was asked to find the general solutions of the two following differential equations:

    Q1. y'''[x] + 2 y''[x] + 5 y'[x] = 0

    Q2. y''[x] + 6 y'[x] + 9 y[x] = 0

    2. Relevant equations

    See above.

    3. The attempt at a solution

    My answers to both problems were of the form y = f[x].

    My professor informed me that the general solution for the differential equation y'''[x] + 2 y''[x] + 5 y'[x] = 0 should not have been of the form y = f[x], but should have been of the form y'[x] = f[x].

    Is this conventional?

    Would that mean the general solution of αy(5)[x] + βy'''[x] = 0 would be of the form y'''[x] = f[x]?

    Thanks for sharing your insight/feedback!

    Jim
     
  2. jcsd
  3. Feb 7, 2012 #2

    ehild

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    Homework Helper
    Gold Member

    The first equation does not include y(x), so it can be solved for y' as a second order de (use y'=z(x) and solve for z). After solving for z(x)=y'(x), you need to integral y' to get y. So the general solution is a function y=f(x) which contains three integration constants.

    ehild
     
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