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Question: substituting new functions

Question:substituting new functions

SandorSzabo 607 Maple
differential-equation substitution
March 21 2008
0

I have an  ode system, and use  2 D Math  (I don't know how to copy here, so I type by hand)

x'(t) = -y(t) + x(t) (1 - x^2(t)  -  y^2(t)),

y'(t) = x(t) + y(t) (1 - x^2(t) - y^2(t)).

I would like to introduce  x(t) = r(t) cos(Theta(t)), y(t) = r(t) sin(Theta(t)) and manipulate the equations further.

The problem is the left hand side. In one case I obtain Dx(t), in the other case (r(t) cos(Theta(t))' without calculation on it.

I ask some help. Thanks.

                                                  Sandor

 
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