3. Check that the polar change of variablesx(t)-r(t)(os0(t),y(t) = r(t) sin0(t)in the system (1) gives the new (and separated) systenmr(t) = r(t)(1-r2(t)),for which r(t) 1,0(t)--t is n solution, and (t)-cos(-t), y(t) = sin(-t) isa periodic solution of (1). Sketch the trajectory (a(t) v(t)) tor t 2 0, showing thedirection: Sketch the trajectories of solutions of (1) starting at the points (1/2, 0) andi(2,0) įlidicating what happens to Lhem when t → oo.

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Asked Apr 1, 2019

pls explain to me step by step. pls pls dont skip any steps. thanks

3. Check that the polar change of variables
x(t)-r(t)(os0(t),
y(t) = r(t) sin0(t)
in the system (1) gives the new (and separated) systenm
r(t) = r(t)(1-r2(t)),
for which r(t) 1,0(t)--t is n solution, and (t)-cos(-t), y(t) = sin(-t) is
a periodic solution of (1). Sketch the trajectory (a(t) v(t)) tor t 2 0, showing the
direction: Sketch the trajectories of solutions of (1) starting at the points (1/2, 0) andi
(2,0) įlidicating what happens to Lhem when t → oo.
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3. Check that the polar change of variables x(t)-r(t)(os0(t), y(t) = r(t) sin0(t) in the system (1) gives the new (and separated) systenm r(t) = r(t)(1-r2(t)), for which r(t) 1,0(t)--t is n solution, and (t)-cos(-t), y(t) = sin(-t) is a periodic solution of (1). Sketch the trajectory (a(t) v(t)) tor t 2 0, showing the direction: Sketch the trajectories of solutions of (1) starting at the points (1/2, 0) andi (2,0) įlidicating what happens to Lhem when t → oo.

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Expert Answer

Step 1

To analyze the given system of differential equations using polar coordinates transformation

Step 2

Express the given system in polar coordinates using the transformation formulae 

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Step 3

We solve for r' and theta ' to obtain the re...

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