Week 4 1st ODE

Question 1

solution method: Integration factor

what form should the ODE be in to use this method?

Answer 1

Where P,Q are arbitrary: constants/ functions of ‘x’, the Denominator/Independent variable/inside bracket

Question 2

What is the integration factor?

Answer 2

Question 3

What is the solution for the integration factor? E.G. dy/dx

Answer 3

Question 4

Solve this ODE

State what solution method you will use

Answer 4

IF

Question 5

Solve this ODE

State what solution method you will use

Answer 5

IF

Question 6

Solve this ODE

State what solution method you will use

Answer 6

IF

Question 7

Solve this ODE

State what solution method you will use

Answer 7

IF

Question 8

What’s the differential equation form ? (e.g. engineering problems)

Answer 8

Question 9

What is Newton’s law of cooling?

Answer 9

rate of change of temp is proportional to the difference between that rate and the surroundings

Question 10

Answer 10

Question 11

Answer 11

Question 12

Classify the following differential equations a) by order b) by whether they are linear or non-linear
and c) if linear, whether they are homogeneous or non-homogeneous

Answer 12

order= 1
(dx/dt is the biggest derivative so = 1)

linear
1- dependent variable (TOP) and its derivatives are only to first degree

2- no products of dependent variable (TOP) with its derivatives

3- no transcendental functions/non-linear functions of x (dependent/TOP) and its derivatives

non-homogenous
(doesn’t = 0 at end, even though it’s in standard form- all x terms LHS )

Question 13

Answer 13

Question 14

Equation for the volumetric flow rate

Answer 14

Q = A * V

A= cross-sectional area

V= velocity

Question 15

Answer 15

Question 16

Answer 16

Question 17

?????