Notes 18 Simple first order differential equations

Question 1

What is a differential equation?

Answer 1

it is defined as the equation that contains derivatives of one or more dependent variables with respect to one or more independent variables.

Question 2

What is the simplest first order differential equation form?

Answer 2

Question 3

How do we solve this simplest form of a differential equation?

Answer 3

Question 4

What can we use the simplest first order differential equation for?

Answer 4

‘the rate of change of some quantitiy is proportional to that quanitiy, ie how much is in that account after t years for example.

Question 5

Answer 5

Question 6

So we use the simplest first order differential equations, for compound interest, future values and also depreciation?

Answer 6

Question 7

What is a separable first order differential equation?

Answer 7

Simply put, a differential equation is said to be separable if the variables can be separated. e.g all the dy and y’s on one side and all the dx’s and x’s on one side.

Question 8

So how do we solve a separable first order differential equation?

Answer 8

Question 9

Answer 9

Question 10

Answer 10

Question 11

What is a linear first order differential equation and what is the form of it?

Answer 11

Question 12

Answer 12

Question 13

Answer 13

Question 14

We have to set up a separable first order differential equation?

Answer 14

Question 15

What does this diagram show?

Answer 15

This is a continous model of price adjustment, which shows the rate at which the price at time t, p(t) changes with time depending on excess supply over demand. In the cobweb model we were given the price at a time, but here we are seeing how the price changes at every moment.

Question 16

What are the 3 cases we can have, in which the firm can decide to do, when taking away excess supply over demand.

Answer 16