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Math Help - Vector Fields

  1. #1
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    Vector Fields

    Verify that the vector field 6 F(x,y) = (x-y)i + (x+y)j has the flow lines given by x(t) = Ae^(t)cos(t+α)i + Ae^(t)sin(t+α)j where A and α are arbitrary real constants.
    Show that the flow lines described follow a generally spiral path, in one case degenerating into a point.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by Playthious View Post
    Verify that the vector field 6 F(x,y) = (x-y)i + (x+y)j has the flow lines given by x(t) = Ae^(t)cos(t+α)i + Ae^(t)sin(t+α)j where A and α are arbitrary real constants.
    We only have to verify \vec{x}\;'(t)=F[\vec{x(t)}] for all t\in\mathbb{R} .

    Show that the flow lines described follow a generally spiral path, in one case degenerating into a point.
    If A=0 , then \vec{x}(t)=(0,0) for all t\in\mathbb{R} .

    Regards.

    Fernando Revilla
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