MATHS 2102 Differential Equations II Written Assignment 5
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MATHS 2102 Differential Equations II
Written Assignment 5
Due: 5.00 pm Monday 29 May
When presenting your solutions to the assignment, please include some explanation in words to accompany your calculations. It is not necessary to write a lengthy description, just a few sen- tences to link the steps in your calculation. Messy, illegible or inadequately explained solutions
may be penalised. The marks awarded for each part are indicated in boxes. This assignment has 1 question(s), for a total of 16 marks.
1. Consider the ordinary differential equation
(1)
(a) Find any singular points of (1).
(b) The point x = x0 = 0 is a regular singular point of (1), hence it has at least one solution of the form
(2)
By substituting (2) and its derivatives into (1):
i. Find the indicial equation and solve it for r .
ii. Determine the recurrence relation for each root of the indicial equation and hence obtain two linearly independent solutions of (1).
iii. Write down a general solution of (1).
Do these calculations by hand. Show all your working.
2023-05-28