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Math Help - Need help solving differential equation

  1. #1
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    Need help solving differential equation

    Hi, can anyone give me some direction how I would about solving this problem?


    Thanks anyone that can help!


    Need help solving differential equation-diff.pdf
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  2. #2
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    The notation may be making the problem more complicated than it appears??:
    I don't think you need to know anything more than \frac{d}{dx}ax^n = anx^{n-1}
    Last edited by mr fantastic; December 25th 2010 at 06:36 PM. Reason: Restored deleted post.
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  3. #3
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    Using induction may make things easier too.
    I've not gone through any calculations, but induction would be my first stab at this.
    Last edited by mr fantastic; December 25th 2010 at 06:36 PM. Reason: Restored deleted post.
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  4. #4
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    Quote Originally Posted by john1990 View Post
    Hi, can anyone give me some direction how I would about solving this problem?


    Thanks anyone that can help!


    Click image for larger version. 

Name:	Diff.pdf 
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ID:	20164
    Here is an image from your attachment:
    (The \displaystyle \alpha_i are real coefficients.)

    I think there is a typo in the expression on the right-hand side of the equation.

    \displaystyle {{d}\over{dz}}\sum_{i=0}^n{{\alpha_i z^i}\over{i!}}

    \displaystyle = {{d}\over{dz}}\alpha_0+\sum_{i=1}^n{{d}\over{dz}}{  {\alpha_i z^i}\over{i!}}

    \displaystyle =0+\sum_{i=1}^n{{(i)\alpha_i z^{(i-1)}}\over{(i)(i-1)!}}

    \displaystyle =\sum_{i=0}^{n-1}{{\alpha_{i+1} z^{i}}\over{i!}}
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  5. #5
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    Quote Originally Posted by SammyS View Post
    Here is an image from your attachment:
    (The \displaystyle \alpha_i are real coefficients.)

    I think there is a typo in the expression on the right-hand side of the equation.

    \displaystyle {{d}\over{dz}}\sum_{i=0}^n{{\alpha_i z^i}\over{i!}}

    \displaystyle = {{d}\over{dz}}\alpha_0+\sum_{i=1}^n{{d}\over{dz}}{  {\alpha_i z^i}\over{i!}}

    \displaystyle =0+\sum_{i=1}^n{{(i)\alpha_i z^{(i-1)}}\over{(i)(i-1)!}}

    \displaystyle =\sum_{i=0}^{n-1}{{\alpha_{i+1} z^{i}}\over{i!}}
    Hi, ye I see that. Ha, what a dummy I am! Should have seen that.

    Cheers.
    Last edited by mr fantastic; December 26th 2010 at 02:37 PM. Reason: dumbass --> dummy
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