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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
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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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.

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.
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
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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