1.) dx dt + 7x = 5 cos 2t 2 ← Equation 1
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Hello, Please EXPLAIN THIS SOLUTION USING ONLY WORDS SO I CAN UNDERSTAND IT BETTER. Thank You. Hoping you will answer it the way i asked.
example: in the first part of this diffetential equation, we should get the .............

Transcribed Image Text:.
1.) dx
dt
Equation 1
dx
dt
+ 7x = 5 cos 2t
2
+ P(t) x =
=
Here PCt) = 7 and Q(t) = 5 cos 12 (t)
has the form
• For the integrating factor I.F
I-F= e Sfutjat
estat
(F-F) X
at)
•
• The general solution
We know that
Sf (t) g(t) at
← Equation 1
751xdt
2 e
- SCI-F.).
7t
⇒ [= coszt
is given by
F.) x Q (t) dt + C; Where Cis
constant
ने
est. x-fe²t. 5 cos 26 db + c
2t
ezt
s fest
S
Let I = √e²tx cos (26) 06
Sezt
x cos (2) dt + c
then let f(t) = cos (2+), g(t) = e7t
• Now
←
I= zt
cos 2+ Sett dt - Sa cos 2+ (feat at ) dt
7t
26
ext
df
f(t) Sgutidt :- Salf
- Solf (Sght) ott) dt
dt
•
ezt -S(-2sınzt).
7
#
an arbitrary
Equation (2)
dt
![크
M
✔
=
ㅗ
(1
e
53
커
99
fent, cos(t) +죽 [ancet), 딸
ㅗt
구
즉 [gin(2t)
et
구
I eft
=> I
cos 25
det, cor(it) 가죽co.net -를 즐 feat.
*cos ㅏ
san 2t
19
Se
t
⇒ I = 99
53
=
+
टात
5
Sett sin (24) dt
en
) (+2) = (Acos2t + 2sin2t)et
99
49
53
cos (2t) + 스
49
●
e
7t
sinzt
-
using equanon 2
5[ㅎㅋ
[ㄶ (Acos2t +2 sin
(7cos 2t + 2sinet) et
거
99
ㅗ (7cos 2t't 2sin 2t) est
53
- Scost at
es
dt
구
쉐
(7cos 2t +2 sın 2t)et
I
ztjet]tc
(Acos2t tisin 2t) tee-t
+
CHROMATR>
Changsen
S
cus 2t alt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F594838af-74e9-41da-ae02-df56efaa43d5%2F26d9a9e1-9960-451d-b98d-cf0f1f456321%2Fwgru88d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:크
M
✔
=
ㅗ
(1
e
53
커
99
fent, cos(t) +죽 [ancet), 딸
ㅗt
구
즉 [gin(2t)
et
구
I eft
=> I
cos 25
det, cor(it) 가죽co.net -를 즐 feat.
*cos ㅏ
san 2t
19
Se
t
⇒ I = 99
53
=
+
टात
5
Sett sin (24) dt
en
) (+2) = (Acos2t + 2sin2t)et
99
49
53
cos (2t) + 스
49
●
e
7t
sinzt
-
using equanon 2
5[ㅎㅋ
[ㄶ (Acos2t +2 sin
(7cos 2t + 2sinet) et
거
99
ㅗ (7cos 2t't 2sin 2t) est
53
- Scost at
es
dt
구
쉐
(7cos 2t +2 sın 2t)et
I
ztjet]tc
(Acos2t tisin 2t) tee-t
+
CHROMATR>
Changsen
S
cus 2t alt
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