Write the homogeneous part of the differential equation system, namely f (x) = g(x) = 0 obtained from the equation on the 1st paper above and written on the 2nd paper, in normal form and solve the resulting system by means of eigen-values and eigen-vectors.
Write the homogeneous part of the differential equation system, namely f (x) = g(x) = 0 obtained from the equation on the 1st paper above and written on the 2nd paper, in normal form and solve the resulting system by means of eigen-values and eigen-vectors.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Write the homogeneous part of the
![Soru :
x>0 olmak üzere tanımlı olan u(x) ve v(x) fonksiyonlarının sağladığı diferansiyel denklem
takımı
(u'(x)+v'(x)– 2u(x)– v(x)–1/x=0
-2u' (х) — v'(х)+и(х) —v(х) — х* —3х+1-0
şeklinde verilmiş olsun.
1
Soruda verilen diferansiyel denklem takımını
[ Lu(x)+L,v(x)= f(x)
|Lu(x)+L,v(x) =g(x)
formunda yazmaya elverişli kılan L, , n=1,2, 3, 4 diferansiyel operatörleri ile f(x), g(x)
fonksiyonlarını belirleyiniz.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17c02bfb-40d8-49c0-aa5e-6c3ae15c1ca8%2Fbf0472a1-c880-4df1-8037-dba27ae90119%2Flsqqgxq_processed.png&w=3840&q=75)
Transcribed Image Text:Soru :
x>0 olmak üzere tanımlı olan u(x) ve v(x) fonksiyonlarının sağladığı diferansiyel denklem
takımı
(u'(x)+v'(x)– 2u(x)– v(x)–1/x=0
-2u' (х) — v'(х)+и(х) —v(х) — х* —3х+1-0
şeklinde verilmiş olsun.
1
Soruda verilen diferansiyel denklem takımını
[ Lu(x)+L,v(x)= f(x)
|Lu(x)+L,v(x) =g(x)
formunda yazmaya elverişli kılan L, , n=1,2, 3, 4 diferansiyel operatörleri ile f(x), g(x)
fonksiyonlarını belirleyiniz.
![Step 1
that uix)+v'( -au(x) -v(x)-=0
-2u'(x) -v'tu(x)-v(x)-x
ー3x +1 ミ
u'(x) +v cx) -241x) -v(x)
-> (
ー2u(x) -(x) +ucx) (x)
ニ)
%3D
2.
ニx +3x -
Step 2
2
Let
D = d
DU(I) + DV(x) - 24(*) -V(x) = L
it
ー2 Du(x)
- Dv(x) + (x) -V(x) =メ+3X-1
(p -)u(x)+(D-4) v(x) =と
-ュD +) u(3) +(-D-Dv«) = ?43x -1
L, u (x) + L2 V cx)
L3u(x) + L4 v(x) = g(x)
=frx)
(x)F ニ
where L, =
L、 こー)
D-2,
L3 =
ーュp
-コD
L4 = - D-|
f(x)- 女
and glx) =
x43x -1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17c02bfb-40d8-49c0-aa5e-6c3ae15c1ca8%2Fbf0472a1-c880-4df1-8037-dba27ae90119%2F9wpythf_processed.png&w=3840&q=75)
Transcribed Image Text:Step 1
that uix)+v'( -au(x) -v(x)-=0
-2u'(x) -v'tu(x)-v(x)-x
ー3x +1 ミ
u'(x) +v cx) -241x) -v(x)
-> (
ー2u(x) -(x) +ucx) (x)
ニ)
%3D
2.
ニx +3x -
Step 2
2
Let
D = d
DU(I) + DV(x) - 24(*) -V(x) = L
it
ー2 Du(x)
- Dv(x) + (x) -V(x) =メ+3X-1
(p -)u(x)+(D-4) v(x) =と
-ュD +) u(3) +(-D-Dv«) = ?43x -1
L, u (x) + L2 V cx)
L3u(x) + L4 v(x) = g(x)
=frx)
(x)F ニ
where L, =
L、 こー)
D-2,
L3 =
ーュp
-コD
L4 = - D-|
f(x)- 女
and glx) =
x43x -1
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