Go back
Another Differential problem

Another Differential problem

Posers and Puzzles

1 edit
Vote Up
Vote Down

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 :'(

1 edit
Vote Up
Vote Down

Originally posted by emanon
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 :'(
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.