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Solve This Differential Equation HELP

  1. Nov 18, 2009 #1
    1. Find the Differential Equation of Function if :
    F(x,y,z)=z^2 ln(x/y)-3e^xy Cothz




    2. Relevant equations



    3.I just don't know where to start ...Shud I find F x and F xx ...Plzz help!
     
  2. jcsd
  3. Nov 18, 2009 #2

    HallsofIvy

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    First, that's not a "differential equation". You are asked to find the first and second partial derivatives of a function with respect to x.

    [itex]F(x,y,z)= z^3 ln(x/y)e^{xy}coth(z)[/tex]

    Since in partial derivatives you treat the "other" variables as constants, you can think of that as
    [tex]F(x)= A ln(x/b)e^{bx}[/tex]
    with [itex]A= z^3 coth(z)[/itex] and b= y. Thats the product of a logarithm and exponential so use the product rule and, of course, the chain rule for the "x/b" and "bx" terms. Don't forget to replace A and b by their expressions in z and y at the end.
     
  4. Nov 18, 2009 #3
    Thanks a lot mate!Really Appreciated it!
     
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