1. ## 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.

2. Originally Posted by Playthious
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