# Homework Help: Solve This Differential Equation HELP

1. Nov 18, 2009

### fan_103

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. Nov 18, 2009

### HallsofIvy

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.

$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 $$F(x)= A ln(x/b)e^{bx}$$ with [itex]A= z^3 coth(z)$ 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.

3. Nov 18, 2009

### fan_103

Thanks a lot mate!Really Appreciated it!

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