Week 7 systems of ODEs

Question 1

What is the matrix form?

Answer 1

First matrix= vector of differentials

Question 2

what is the eigenvalue problem?

Answer 2

Question 3

what is the vector prime equation?

how does it relate to the matrix form?

Answer 3

Question 4

What’s the equation for the general solution?

Answer 4

Question 5

Solve this system of 1st Order Linear ODE

Answer 5

1) write in matrix form

2) make substitution of trial function

3) leads to eigenvalue problem

4) compute the eigenvalues (only focus on the determinant of lambda I - A

5) Compute the eigenvectors

6) sub values of lambda + eigenvectors into general solution

Question 6

What is the trial function

Answer 6

Question 7

Solve this system of 1st Order Linear ODE

Answer 7

Question 8

Solve this system of 1st Order Linear ODE

Answer 8

Question 9

What’s the equation for the general solution? (2nd Order)

Answer 9

Question 10

Solve this system of 2nd Order Linear ODE

(note 2y2 on second equation)

Answer 10

Question 11

what’s the square root of -1?

Answer 11

i

(imaginary number)

Question 12

Solve this system of 2nd Order Linear ODE

Answer 12

Question 13

What’s the general solution equation for negative eigenvalues ? (negative lambda values)

Answer 13

Question 14

what’s the square root of -6?

Answer 14

separate the -ve sign, by putting ‘i’ outside of square root

Question 15

Assumptions for the liquid filled tank

Answer 15

• substance is instantly and uniformly dissolved in the tank (well-mixed)