MAT3700 Assignment 2 Memo | Due June 2026

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l(SSl6NMENT1 2
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DUE: JUNE 2026 +




DISCLAIMER: iI I I
- rHrS7lrlt:OMENT I DR7lEFERENCE AND11Ul ~CE PUR SE

ACADEMIC MISCONDUCT RESULTING FROM THEIR USE. IT IS YDURi
_IIESPDNSIBILITY T_! ENsut DRIGINALJTY ANq COMPLIANCE WITH
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ONLY. I DD NDTtTAKE RESPbNSIBILITY~FDR AN~-PLAGIARl~M- tMISUSE. DR

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RELEVANT GUIDELINES DR STANDARDS.

, PLEASE USE THIS DOCUMENT AS A GUIDE ONLY

 QUESTION 1

Question 1.1

11. Complementary Functiion (ye)
Set 'the dli ar-acterist[c equation to zero:


2
m- -4m 4 == 0



( ni ·- 2')• == 0 ===;> m == 2 (rep ea ed root )
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2. P,aliticu1lfa r lri I egrali (yp)
'Sp lit the right and sid e mto tw o parts: "]Jp = '!Jp1
1 Yrtl.•

0
'
Fo r Y;p1 1 ;:!;i: .
= (D - :2] :.i •

Us~ng 1e· s Lrule 7{DJ e.ail:
• .,,.._
1u
·
n ·· ii, H • ].
= e az Jtbl ) •• J:

2;x 1 X l
y '1 == e D _+_2_') = -2-) - 1 == ,e -D' ~l
-((_

lntegratiing 1 twice wan respect to ·:


Y e 2x ( _· - 2 )· -_ ,X 2 e2x
pl== -2 ' 2


0 For
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y·P. ' -- lP - •1liD . ~ - :2.:c .
OJ;;- •


Substitute D = - 2:

l - ~X
l - ·2x 1 -2
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YP (-2)2 - 4(- ·2 . 4e 4 ,8 4,
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