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Math 3411-^ Quiz ft*/.BCfAg
Problem#2 is on the back. Name
-"- Bf e-'t
- Let u: t5 and u :^ s-2t.
(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?
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= o + t.
t r - 5 1 2 t u + M l - b z
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- Two linearlyindependentsolutionstoy" -2t-2y:0^ on (0,oc) are givenby u-t2 and o l _^ f^ , _ l _
(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 3
- 3 (^) - s w 'l-u (^) ; -a (^) s'' t q K ^ -^ 3 i t
? 3
= t ' - s
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
