MAT3700 Assignment 02 Answers Year 2026

Mathematics III (Engineering)

Assessment 2 Answers

Year 2026




0027 68 628 1800

,
, QUESTION 1


1.1
(𝐷2 − 4𝐷 + 4)𝑦 = 𝑒 2𝑥 + 𝑒 −2𝑥
𝐷2 − 4𝐷 + 4 = 0
(𝐷 − 2)2 = 0
𝐷 = 2 𝑡𝑤𝑖𝑐𝑒
𝑦𝐶.𝐹 = 𝐴𝑒 2𝑥 + 𝐵𝑥𝑒 2𝑥


1
𝑦𝑝 = {𝑒 2𝑥 + 𝑒 −2𝑥 }
𝐷2 − 4𝐷 + 4

1 1
= {𝑒 2𝑥 . 1} + 2 {𝑒 −2𝑥 }
𝐷2 − 4𝐷 + 4 𝐷 − 4𝐷 + 4


1 1
= 𝑒 2𝑥 . {1} + {𝑒 −2𝑥 }
(𝐷 + 2)2 − 4(𝐷 + 2) + 4 2
(−2) − 4(−2) + 4


1 1
= 𝑒 2𝑥 . {1} + 𝑒 −2𝑥
𝐷2 + 4𝐷 + 4 − 4𝐷 − 8 + 4 16

1 1 −2𝑥
= 𝑒 2𝑥 . {1} + 𝑒
𝐷2 16
1 1
𝑦𝑝 = 𝑥 2 𝑒 2𝑥 + 𝑒 −2𝑥
2 16
𝟏 𝟏 −𝟐𝒙
𝒚𝒈𝒆𝒏 = 𝑨𝒆𝟐𝒙 + 𝑩𝒙𝒆𝟐𝒙 + 𝒙𝟐 𝒆𝟐𝒙 + 𝒆
𝟐 𝟏𝟔