ODE help agian

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  1. HappyHammer15's Avatar
    1 25-05-2012  23:09
    • Junior Member
    • Posts: 45
    ODE help agian
    I have another question regarding ODE and reduction of order

    http://img96.imageshack.us/img96/4223/eqn2.png

    I get

    x^5 g'(x) + (2x^4 +x^3)g(x) = 0

    Rearranging and integrating gives:

    ln g(x)= -2ln(x) -\frac{1}{x}

    so g(x)=x^{-2} - e^{\frac{1}{x}}

    However, I have to integrate this again to find f(x) which isnt possible.
    I must have made a mistake. Can someone help me determine where.

    Thanks
  2. nuodai's Avatar
    2 25-05-2012  23:15
    • PS Helper
    • TSR Legend
    Re: ODE help agian
    For starters e^{-2\ln x - \frac{1}{x}} \ne x^{-2} - e^{\frac{1}{x}}, but also I think your -\dfrac{1}{x} should be +\dfrac{1}{x}.

    I haven't followed through the working from the start though - I have no idea what your g is, for instance, so I don't know whether you've made mistakes earlier on. But if you fix the above errors you'll get something you can solve, presuming you need to integrate g to get f.
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