Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Practice Quiz 5 Solutions - Differential Equations | MATH 3411, Quizzes of Differential Equations

Material Type: Quiz; Class: DIFFERENTIAL EQUATIONS; Subject: Mathematics; University: Armstrong Atlantic State University; Term: Unknown 1989;

Typology: Quizzes

Pre 2010

Uploaded on 08/04/2009

koofers-user-8pv
koofers-user-8pv 🇺🇸

10 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
T t
lr,lot
Math 3411
- Quiz
ft*/.BCfAg
Problem
#2 is on the back. Name
-"- Bf e-'t
1. Let u: t5 and
u : s-2t.
(a) Calculate the Wronskian of u and u.
(b) If u and
u are
to be linearly
independent
solutions
of.
y" + pA'
+ qA: 0 on some
interval .[, what values of. t cannot be in the interval f?
i( ^ ",,,/ v a4( /'rtu| /\
fTra^ fTrL wronsk^ (annol
- J
ttg'",- st4e'" c
Q
ta
e'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.
-+
tr-512 tu+Ml- bz
aL
o*./ v a# /ric*r$
pf2

Partial preview of the text

Download Practice Quiz 5 Solutions - Differential Equations | MATH 3411 and more Quizzes Differential Equations in PDF only on Docsity!

T t l r , l o t

Math 3411-^ Quiz ft*/.BCfAg

Problem#2 is on the back. Name

-"- Bf e-'t

  1. 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?

i( ^ ",,,/

v a4( /'rtu| /\

fTra^ fTrL^ wronsk^^

(annol

  • J ttg'",- st4e'"

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$

tfunPpinl"*

Vb P'IM

  1. 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 =

  1. ,
  • t , l = - l - a = - 3

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