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MAT244 Math--Lectures / fast method of solution of linear equations (Handout 8 method)

« on: December 07, 2014, 10:30:12 AM »

Handout 8 introduced a fast method of solving linear equations with constant coefficient.
The example used was of repeated roots, where Q( r)=Q`( r) = 0.
I am wondering for a question like Problem 3 in Term test 1, how can we apply this method?
I tried to apply the equation but I got a solution of particular solution totally different from the answer key.
something like (3t^2 - 5t^2 e^(-2t))/(5t-1)

Thanks.

2

MAT244 Math--Lectures / Homework 9.3 Question 16

« on: December 04, 2014, 09:26:49 PM »

For Q16 on 9.3, phase portrait shows that xy tends toward a circle. I attached the picture below.
By definition of a critical point, I only found (0,0) but I feel like the circle related to 1-x^2-y^2 behaves similar as critical point.
How should I show that in the solution? Could anyone lead me with some procedure?
Thanks in advance.