need help finding y′′+4y′+5y=5x+3e^(-x) The other doc is a similar problem to help solve the first one
need help finding y′′+4y′+5y=5x+3e^(-x) The other doc is a similar problem to help solve the first one
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
need help finding y′′+4y′+5y=5x+3e^(-x)
The other doc is a similar problem to help solve the first one
![a. Find a particular solution to the nonhomogeneous differential equation y " + 4y' + 5y = 5x + 3e».
Yp
help (formulas)
b. Find the most general solution to the associated homogeneous differential equation. Use c and c2 in your answer to
denote arbitrary constants, and enter them as c1 and c2.
Yh =
help (formulas)
c. Find the most general solution to the original nonhomogeneous differential equation. Use c and c, in your answer to
denote arbitrary constants.
y =
help (formulas)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde00a360-9ad2-4257-a7ee-1eaea5a279d3%2Fb5128419-fa59-4bfa-b768-d751498b9b17%2F3m9476n_processed.png&w=3840&q=75)
Transcribed Image Text:a. Find a particular solution to the nonhomogeneous differential equation y " + 4y' + 5y = 5x + 3e».
Yp
help (formulas)
b. Find the most general solution to the associated homogeneous differential equation. Use c and c2 in your answer to
denote arbitrary constants, and enter them as c1 and c2.
Yh =
help (formulas)
c. Find the most general solution to the original nonhomogeneous differential equation. Use c and c, in your answer to
denote arbitrary constants.
y =
help (formulas)
![y" +Hly'+ Sy= 15x + 3e=X
--
La=-l,w=0,r= - |
Solve =0
check for
repeats
= e* cos (x)
-ax
- 2x
no repeats
Ansatz
tríal salutim
+ CeX
y'=B- Cex
y"= Cex
5A +4B) + (5B)x + (sc-4c re)e?
(22)e -*
3 e*
y"tly' +5y
= (5A+4B) + (5B)x
I5 x
want =
5B=15→ B=3
2c=3 →C=2
5A+413)=0→ A= -12/5
12
-2K
cle
-2X
+ 3x +(3)c](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde00a360-9ad2-4257-a7ee-1eaea5a279d3%2Fb5128419-fa59-4bfa-b768-d751498b9b17%2Fsgju0sk_processed.png&w=3840&q=75)
Transcribed Image Text:y" +Hly'+ Sy= 15x + 3e=X
--
La=-l,w=0,r= - |
Solve =0
check for
repeats
= e* cos (x)
-ax
- 2x
no repeats
Ansatz
tríal salutim
+ CeX
y'=B- Cex
y"= Cex
5A +4B) + (5B)x + (sc-4c re)e?
(22)e -*
3 e*
y"tly' +5y
= (5A+4B) + (5B)x
I5 x
want =
5B=15→ B=3
2c=3 →C=2
5A+413)=0→ A= -12/5
12
-2K
cle
-2X
+ 3x +(3)c
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