# Another Differential problem

emanon
Posers and Puzzles 09 May '07 13:13
1. emanon
Student
09 May '07 13:131 edit
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 :'(
2. PBE6
Bananarama
09 May '07 18:161 edit
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.