MAT3700 Assignment 02 Answers Year 2025

Mathematics III (Engineering)

Assignment 2 Answers

Year 2025




0027 63 985 5033

,
, QUESTION 1


1.1

(𝐷 2 − 6𝐷 + 9)𝑦 = 𝑒 3𝑥 + 𝑒 −3𝑥

𝐷 2 − 6𝐷 + 9 = 0

(𝐷 − 3)2 = 0

𝐷 = 3 𝑡𝑤𝑖𝑐𝑒

𝑦𝐶.𝐹 = 𝐴𝑒 3𝑥 + 𝐵𝑥𝑒 3𝑥


1
𝑦𝑝 = {𝑒 3𝑥 + 𝑒 −3𝑥 }
𝐷 2 − 6𝐷 + 9


1 1
= {𝑒 3𝑥 . 1} + 2 {𝑒 −3𝑥 }
𝐷2 − 6𝐷 + 9 𝐷 − 6𝐷 + 9


1 1
= 𝑒 3𝑥 . {1} + {𝑒 −3𝑥 }
(𝐷 + 3)2 − 6(𝐷 + 3) + 9 2
(−3) − 6(−3) + 9


1 1
= 𝑒 3𝑥 . {1} + 𝑒 −3𝑥
𝐷2 + 6𝐷 + 9 − 6𝐷 − 18 + 9 36


1 1 −3𝑥
= 𝑒 3𝑥 . {1} + 𝑒
𝐷2 36

1 1
𝑦𝑝 = 𝑥 2 𝑒 3𝑥 + 𝑒 −3𝑥
2 36

𝟏 𝟏 −𝟑𝒙
𝒚𝒈𝒆𝒏 = 𝑨𝒆𝟑𝒙 + 𝑩𝒙𝒆𝟑𝒙 + 𝒙𝟐 𝒆𝟑𝒙 + 𝒆
𝟐 𝟑𝟔