Find a particular solution of y" +9y+14y = 8e-2x
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
The ANS is yp=8/5xe^(-2x).
I have attached what I have so far. Thx
Transcribed Image Text:(b) Find a particular solution of
y" +9y' + 14y = 8e-2x
![-2X
yp = Axe²
ур
= -2Axe
+ Ae
-2x
-2x
-2x
4 Axé
нахе2х
yp = -2Ae
тчахе
- 2 Ae
= -4Ae
- 2x
-2x
-2x
-2x
-2x
ANS: A = 8
5
+4 Axe
+91-2 Axe-2x + Ae¯2x) + 14(-44€2
-2X
-18 Axe 2x +q Ae?
-56 Ae
-2x
qAe
урах) = в хе
_2x
-2x
-2x
+ ²Axe ²x) = 8e3
-56 Ae-2x =
+56 Axé
-2x
Ee
-47A= 8
A
-2x
=-8
47
-2x
=&e
-A[x46² +
de
dx
yp =
-2x
= -2Axe
-2x
-2Axe
-2x
-24 [ x]
хе
-2x
+ Ae
2x
-24 [x - 1₂²x + 4x-2²]
d
dx
dx
dx
-24 [x-25** + e-²x]
-2x
-2 Ae-2x + чахе](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca6b5de9-d666-4be4-bec5-372f49facd74%2Fbd3af8a3-e2dc-40b0-a021-ae3163b1e026%2Fskj3s1m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:-2X
yp = Axe²
ур
= -2Axe
+ Ae
-2x
-2x
-2x
4 Axé
нахе2х
yp = -2Ae
тчахе
- 2 Ae
= -4Ae
- 2x
-2x
-2x
-2x
-2x
ANS: A = 8
5
+4 Axe
+91-2 Axe-2x + Ae¯2x) + 14(-44€2
-2X
-18 Axe 2x +q Ae?
-56 Ae
-2x
qAe
урах) = в хе
_2x
-2x
-2x
+ ²Axe ²x) = 8e3
-56 Ae-2x =
+56 Axé
-2x
Ee
-47A= 8
A
-2x
=-8
47
-2x
=&e
-A[x46² +
de
dx
yp =
-2x
= -2Axe
-2x
-2Axe
-2x
-24 [ x]
хе
-2x
+ Ae
2x
-24 [x - 1₂²x + 4x-2²]
d
dx
dx
dx
-24 [x-25** + e-²x]
-2x
-2 Ae-2x + чахе
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