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Material Type: Quiz; Class: DIFFERENTIAL EQUATIONS; Subject: Mathematics; University: Armstrong Atlantic State University; Term: Unknown 1989;
Typology: Quizzes
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Math 3411-^ Quiz ft*/.BCfAg
Problem#2 is on the back. Name
-"- Bf e-'t
(a) Calculate the Wronskian of u and u.
(b) If u and u are to be linearly independentsolutionsof.y" + pA' (^) + qA: 0 on some interval .[, what valuesof.t cannot be in the interval f?
i( ^ ",,,/
v a4( /'rtu| /\
fTra^ fTrL^ wronsk^^
(annol
c Q
tae'o' L^a
L-5l --o
= ) f - - o^ - (^
' > t - 5
ao'
,llt (^) u+(us t=o ^*r/
i,^ a^!^ ,;W"l^ o^ wl^'o/^
fuft""/t"/ 6zr T,
/oe 3enu 3rl'^
{ra T
= o + t.
t r - 5 1 2 t u + M l - b z
aL o./ v a#^ /ricr$
(a) Construct the Green'sfunction associatedrvith P(D) :Dz - (^) 2t-27.
/ r^ l lr^ < \^ z u l e ) ( l t ) - + < / t ) v ( l^ ' '^ l t z^ i^1 L , o , L , T
) w =
4o (^) 6 .1t, t)
? 3
7 t t
( b ) I f f o : 1 a n d (^) / ( t ) : + , e x p r e s s^ t h e (^) r e s ts o l u t i o no f A , , - 2 t - 2 y : / i n t e r m so f U the Green'sfunction and /(t). Do not evaluatethe integral.
r , , /^
t , \t) = L G(t,3)(/4ls d J L o
( t (^) t 3 - < v c
/ 1 \ s t 5 L