Only through the elimination method by using the operators obtained in the solution paper above, obtain the differential equations provided by the functions u(x) and v(x)
Only through the elimination method by using the operators obtained in the solution paper above, obtain the differential equations provided by the functions u(x) and v(x)
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
Only through the elimination method by using the operators obtained in the solution paper above, obtain the differential equations provided by the functions u(x) and v(x)
![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.
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%2Fb5912419-40d8-49b7-ba68-5644dc090a1e%2Fyun5vh9_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.
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.
![Given that u'(x)+v'ro) -aucox) -v(x)-=0
ー3x +1 =o
u(x) +v(s) -2u(x) -V(z) =ー
ニ)
-2u'1x) -v'cx) +ucx) r(x)
2
ニx +3x-
Let
D = d
DU(I) + DV(x) – 24(x) -V(x) =L
そ
ー2 Du(x) - Dv(x) +4(x) -V(x) =x+32-1
(D -2)U (x) + (D-2) v(x) =t
ニ)
+ (-D -Dvx) = x²+3x-1
{
L, u (x) + L2Vc3x) =Frx)
L34(x) + L4 v(x) = g(2)
where L, =
L、 こー)
D-2,
= -20 41
La = -D-|
ーコ
f(x)- 女
and 3(x)ミ x+3x -)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17c02bfb-40d8-49c0-aa5e-6c3ae15c1ca8%2Fb5912419-40d8-49b7-ba68-5644dc090a1e%2Feutdu8o_processed.png&w=3840&q=75)
Transcribed Image Text:Given that u'(x)+v'ro) -aucox) -v(x)-=0
ー3x +1 =o
u(x) +v(s) -2u(x) -V(z) =ー
ニ)
-2u'1x) -v'cx) +ucx) r(x)
2
ニx +3x-
Let
D = d
DU(I) + DV(x) – 24(x) -V(x) =L
そ
ー2 Du(x) - Dv(x) +4(x) -V(x) =x+32-1
(D -2)U (x) + (D-2) v(x) =t
ニ)
+ (-D -Dvx) = x²+3x-1
{
L, u (x) + L2Vc3x) =Frx)
L34(x) + L4 v(x) = g(2)
where L, =
L、 こー)
D-2,
= -20 41
La = -D-|
ーコ
f(x)- 女
and 3(x)ミ x+3x -)
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