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Math Help - Help rewriting a differential equation

  1. #1
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    Help rewriting a differential equation

    Hey, hope someone will help me

    I need some help to rewrite a differential equation.

    I start with the expression :

    Help rewriting a differential equation-1.png

    This reason why this apply (correct me if I'm wrong) is this:

    Help rewriting a differential equation-2.png



    Furthermore this applies:


    Help rewriting a differential equation-3.png

    This I can't explain, if someone could explain to me why and how (detailed if possible), it would be great.
    Sorry if it is obvius, but I'm new to this.

    Thanks
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  2. #2
    Junior Member
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    Re: Help rewriting a differential equation

    \frac{d}{dx} (\frac{d\psi}{d\zeta} \frac{d\zeta}{dx})= (\frac{d}{dx}\frac{d\psi}{d\zeta}) \frac{d\zeta}{dx}+ (\frac{d}{dx}\frac{d\zeta}{dx}) \frac{d\psi}{d\zeta})=(\frac{d^2\psi}{d\zeta^2} \frac{d\zeta}{dx})\frac{d\zeta}{dx}+(\frac{d^2 \zeta }{dx^2}) \frac{d\psi}{d\zeta}
    Your expression misses the second term above.

    By the way for the first equality your wrote it's just the chain rule, Chain rule - Wikipedia, the free encyclopedia
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  3. #3
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    Re: Help rewriting a differential equation

    I'm not quite sure how you get that.. But i came up with this, bacause of what you wrote:

    Help rewriting a differential equation-1.png

    I think this is the solution? Is this properly written mathematically?
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  4. #4
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    Re: Help rewriting a differential equation

    I think you should also read about Leibniz product derivation formula, here:
    Product rule - Wikipedia, the free encyclopedia
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  5. #5
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    Re: Help rewriting a differential equation

    Okay, Thanks, I'll look in to it..

    - But is what I have done wrong? I'm just wondering, since i get the right result..
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