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Math Help - Solve ODE by Power Series - Singular Point

  1. #1
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    Solve ODE by Power Series - Singular Point

    Hi all,

    So I am just wondering if anyone can confirm that the following is a solution of the DE. I'm not entirely sure how to differentiate a factorial so I am at crossroads for checking to see if it satisfies the DE. This was a question off an exam I wrote this morning, and I'm just wondering if that solution is indeed correct.

    xy'' + y' - x^2y = 0

    Solution = 1 + \sum^{\infty}_{n=1}{\frac{x^{3n}}{(n^2)!}

    Thanks in advance!
    Last edited by sjmiller; March 11th 2013 at 12:07 PM.
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  2. #2
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    Re: Solve ODE by Power Series - Singular Point

    y=a+b*x+c*x^2+d*x^3+e*x^4...
    y'=b+2c*x+3d*x^2+4e*x^3 and so on ...you equate multipliers in both sides of DE...
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  3. #3
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    Re: Solve ODE by Power Series - Singular Point

    Quote Originally Posted by sjmiller View Post
    Hi all,

    So I am just wondering if anyone can confirm that the following is a solution of the DE. I'm not entirely sure how to differentiate a factorial so I am at crossroads for checking to see if it satisfies the DE. This was a question off an exam I wrote this morning, and I'm just wondering if that solution is indeed correct.

    xy'' + y' - x^2y = 0

    Solution = 1 + \sum^{\infty}_{n=1}{\frac{x^{3n}}{(n^2)!}

    Thanks in advance!
    You don't need to differentiate the factorial, it's a constant. x is the variable.
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