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Math Help - [SOLVED] Conservative Vector Fields

  1. #1
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    [SOLVED] Conservative Vector Fields

    Hello, can someone please help me with this one...

    Find a nonzero function h for which

    F(x,y) = h(x)[xsin y + y cos y]i + h(x)[x cos y - y sin y]j

    is conservative.

    Thanks!
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  2. #2
    MHF Contributor Calculus26's Avatar
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    The condition you need to satisfy is df/dy = dg/dx (these are actually partial derivatives

    df/dy = h(x){xcos(y) -ysin(y)} +h(x)cos(y)

    dg/dx = h ' (x){xcos(y) -ysin(y)} + h(x)cos(y)

    Setting the two equal we obtain h ' (x) = h(x)

    or h(x) = e^x
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