Solve This Differential Equation HELP

[fan_103]

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

Homework Equations

3.I just don't know where to start ...Shud I find F x and F xx ...Plzz help!

 

[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.

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

 

[fan_103]

Thanks a lot mate!Really Appreciated it!