#### Posers and Puzzles

Leuven

- Joined
- 21 Apr '07
- Moves
- 19119

Is the differential of z = xe^(y^2)

e^(y^2)dx + 2yxe^(y^2)dy ?ðŸ˜•

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 :'(

False berry

- Joined
- 14 Feb '04
- Moves
- 28719

*Originally posted by emanon*

**Is the differential of z = xe^(y^2)
**

e^(y^2)dx + 2yxe^(y^2)dy ?ðŸ˜•

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 :'(

First part looks right. Here's a link that might help with your second question:

http://en.wikipedia.org/wiki/Homogeneous_differential_equation

Looks like the equation you've described is a first-degree homogeneous equation.