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    Hey guys,

    So I'm currently finishing off PDE's and I'm at this question:

    Name:  PDE's question.gif
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    I've been able to get a general solution of:

    u(x,y)= \alpha xy + \beta x + \gamma y + \delta + \displaystyle\sum_{\mu=1}^{\inft  y} (A_{\mu} cos (\mu x) +B_{\mu} sin(\mu x) )(C_{\mu} cosh (\mu y)+D_{\mu} sinh(\mu y) )

    Now I've been able to get the use the first two conditions to get a more specific solution:

    u(x,y)= \displaystyle\sum_{\mu=1}^{\inft  y} (B_{\mu} sin(\dfrac{(2n-1)x}{2L}) )(C_{\mu} cosh (\dfrac{(2n-1)y}{2L}))+D_{\mu} sinh(\dfrac{(2n-1)y}{2L})))

    Now I'm at the next condition:

    u_y(x,0) +u(x,0) =0

    And I'm assuming it's to do with the constant at the beginning of the coshy, but I'm not sure how to progress before I perform the fourier series :unsure:

    Thanks for reading And apologises for typos
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    Are you sure your solution you've got so far is correct, because there isn't an x term in the series at all.
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    (Original post by Noble.)
    Are you sure your solution you've got so far is correct, because there isn't an x term in the series at all.
    Apologises, copying error
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    (Original post by cpdavis)
    Apologises, copying error
    No problem. What is it you're struggling to get with the third condition? Am I simplifying the problem a bit too much, what do you get what you partially differentiate w.r.t y, then set y=0 and add on your specific solution with y=0? Does that get you nowhere?
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    (Original post by Noble.)
    No problem. What is it you're struggling to get with the third condition? Am I simplifying the problem a bit too much, what do you get what you partially differentiate w.r.t y, then set y=0 and add on your specific solution with y=0? Does that get you nowhere?
    Oh **** of course :facepalm:

    forgot to put in y=0 :sigh:

    Okay, now I have: \mu_n D_n = -C_n My gut instinct is to set either D or C to 1, but I can't think of a valid reason :unsure:

    This question is so tedious :sigh:
 
 
 
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