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.

Question

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.

Image Transcription

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.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times vary by subject and question complexity. Median response time is 34 minutes and may be longer for new subjects.

Related Advanced Math Q&A

Find answers to questions asked by student like you

Q: Determine a lower bound for the radius of convergence of series solutions about the given point x0 f...

A: Given:The differential equation is (x2-2x-3)y”+xy’+4y=0

Q: Pls explain to me step by step and pls dont skip any step. Thanks

A: To prove that the taxicab distance is actually a metric on the plane

Q: Abstract Algebra (Proof writing): Looking for assistance on this problem.

A: Consider the function φ:Z/6Z ->Z6  ,

Q: Roche Biotech provides company cars for it's salespeople that cost an average of $25,000. Using the ...

A: To calculate the depreciation expense for the desired year.

Q: 5.2.6.C          Discrete Mathematics This is a dublicate please answer the question as quickly as p...

A: Known fact:Proof for strong induction hypothesis.Base: Show that P(1) is true.Induction: If P(1) and...

Q: Differential equations problem. Please refer to attached image.

A: (a) The function is given as

Q: I am stuck on a question from my history of math textbook. Here is the question: The division of a l...

A: As per norms , the first three parts a,b and c are answered. The problem pertains to the constructio...

Q: At age 22​, someone sets up an IRA​ (individual retirement​ account) with an APR of 8​%. At the end ...

A: Formula used:Future value of an ordinary Annuity:

Q: Explain why you know that λ is a root of charL(x) if and only if Ker(λId-L)≠0

A: To prove the equivalent conditions on the roots of the characteristic polynomial and the kernel of t...