1. Standard memberemanon
    Student
    Leuven
    Joined
    21 Apr '07
    Moves
    19119
    09 May '07 13:131 edit
    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 :'(
  2. Standard memberPBE6
    Bananarama
    False berry
    Joined
    14 Feb '04
    Moves
    28719
    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 ?😕

    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.