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Posers and Puzzles

Posers and Puzzles

  1. Standard member emanon
    Student
    09 May '07 13:13 / 1 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 member PBE6
    Bananarama
    09 May '07 18:16 / 1 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.