MAT3700 Assignments 02 Due 2026

UNIVERSITY OF SOUTH AFRICA
College of Science, Engineering and Technology


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MAT3700: Mathematics III (Engineering)

Assignment 02 — 2026

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MAT3700
Module Code:
Mathematics III (Engineering)
Module Name:
Assignment 02
Assignment:
2026
Due Date:
60
Total Marks:




Submitted in partial fulfilment of the requirements for MAT3700 — UNISA 2026

, UNISA | MAT3700 Assignment 02 – 2026



Question 1

Find the general solutions of the following differential equations using D-operator methods.


1.1


(D2 − 4D + 4)y = e2x + e−2x

(8)


Solution


Step 1: Auxiliary equation



m2 − 4m + 4 = 0 ⇒ (m − 2)2 = 0 ⇒ m = 2, 2


Step 2: Complementary function



yc = (C1 + C2 x)e2x


Step 3: Particular integral

For e2x : Since m = 2 is a repeated root of order 2, multiply by x2 :


1 2x x2 2x x2 2x
yp1 = e = e = e
(D − 2)2 2! 2

For e−2x : Substitute D → −2 (no repeated root):


1 1 1 −2x
yp2 = e−2x = e−2x = e
(D − 2)2 (−2 − 2)2 16

Step 4: General solution


x2 2x 1 −2x
y = (C1 + C2 x)e2x + e + e
2 16




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