APM3706 ASSIGNMENT 04 (Exceptional Solution) Due July 2025

APM3706
ASSIGNMENT 04
Due July 2025

, lOMoAR cPSD|41752181




STUDY GUIDE: CHAPTERS 6, 7 and 8

Answer All Questions
In All assignments we may mark all or few of those questions.

Question 1

Solve Exercise 6.7 from SG.


Question 2

Solve second part of Exercise 6.11 (I mean 6.11- 2(a) and 2(b))from SG.


Question 3

Solve question 3 of Exercise 7.5 from SG.


Question 4

Classify the critical points of the plane autonomous system corresponding to the second
order nonlinear differential equation: ẍ + µ( x2 + 1) ẋ + x= 0 .



Question 5

, ) of each system below.
Determine the type and stability or the critical point at (0 0


(a). X˙ , (b). X˙ , .

, APM3706

ASSIGNMENT 04

Due July 2025



Question 1: Exercise 6.7

Problem: Given X( t) = et e2 t, determine the coefficients Xksuch that:


.

First, simplify the given expression: et e2 t= e3 t. The Maclaurin series expansion for eatis:


.

For e3 t, set a= 3:


.



By comparing this with , we identify:

To verify, compute a few terms:



• For

• For .

These results align with the expansion of e3 t.

Answer:


.