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
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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)
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
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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