Differential Equation: Lecture 3

In lecture 3, you learnt about two main concepts.

1. What is the family of curves?

2. How to model a question using DE and solve the problem?

1. Family of curves

The general solution of a DE can be represented by a set of curves graphically ( one curve for each value of the arbitrary constant). This set of curve is called the family of solution curves of the DE.

A particular solution of the DE corresponds to one specific curve in the family.

When you are asked to sketch the family of curves, you usually choose C=-1, 0 and 1 unless otherwise specified by the question.

Please use G.C. to help you in the sketching!!!

2. Modelling using DE

DE can be used to model a lot of real-life problems including physical phenomenon, process, human behaviours and population growth.

To model a problem with DE, follow the steps below.

Step 1: look for phrases like " the rate of increasing/decreasing of ... is proportional to ..." or ".... is increasing/decreasing at the rate proportional to... "

These phrases give you the Differential Equation.

Step 2: Solve the DE, usually by direct integration. The solution usually has some unknown constants.

Step 3: Use the given data in the question to find out the unknown constants.

After lecture 3, you will be able to do the whole tut11b if you are good at modelling. However you might wanna attempt Q1, 2, 3 , 6 first since they are similar to what we have gone through in the lecture.