Originally posted by emanonFirst part looks right. Here's a link that might help with your second question:
Is the differential of z = xe^(y^2)
e^(y^2)dx + 2yxe^(y^2)dy ?😕
EDIT:
If homogeneous, find the degree of homogeinity of the function:
f(x,y) = xg(y/x), where g is an arbitrary function of one variable.
>no idea how to solve this< all I end up with is txg(ty/tx)...g(ty)?
Don't go studying economics :'(
http://en.wikipedia.org/wiki/Homogeneous_differential_equation
Looks like the equation you've described is a first-degree homogeneous equation.