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Math Help - Differential equations

  1. #1
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    Differential equations

    ok so i've been given the equation
    (S=integrate between infinity and 0 and n = pi)

    S(sin(ax)/sinh(bx))dx = (n/2b)tanh(na/2b)

    and have been told to take a derivative of it in order to evaluate the following

    S(xcos(ax)/sinh(bx))dx

    am I correct in thinking that i simply need to differentiate the right hand side of the above with respect to a in order to get my answer or should i be differentiating with respect to b as well?

    I have been given the result that:

    if S (f(t,x)) dt = A(x)

    then S {d[f(t,x)]/dx}dt = A'(x)

    but wondered if this can be applied to functions with a third variable such that:

    if S (F(t,x,y)) dt = A(x,y)

    then S {dF/dy +dF/dx}dt = dA/dx + dA/dy

    Or am I barking up the wrong tree?
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  2. #2
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    Quote Originally Posted by macabre View Post
    ok so i've been given the equation
    (S=integrate between infinity and 0 and n = pi)
    What n? What does that mean here?
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  3. #3
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    S(sin(ax)/sinh(bx))dx = (n/2b)tanh(na/2b)



    'n' in the above part i have used to represent the value 'pi' as i couldn't find the correct symbol for it

    (as in the one thats roughly 22/7, related to circles etc)
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