Unformatted text preview: in in the class!
' 6. Solve the differential equation
/ 3y" + 2y'  8y = 5 cos x
for both the complementary function and the particular solution. 7. (i) Apply the Frobenius method to obtain the series solutions of the differential
equation (ii) Next, making a substitution such as y (x) = I(x) z (x), put the above equation
into the form
z Q (x) z and apply the WKB method to determine the asymptotic behavior of the function z (x),
and hence ofy (x), as x goes to infinity. C. 00 ~
'rI=/ I "If I 2Jr ~  . (S(d)I 2 ?zL](lh1 L( .(~t ~() v"/ 7T ~() I I I
. I I 2. ,. " ~ .•. \ (2 h i) (z,.,+/) LI [ (?n)  .2..n 2 . (~. !J L I) L (z,,+,) h. (1\ !)~fA:. L tt~ A.e rlJhA'J., "jn/ /r 3. f)l 1t~~ J..t ~ 1 lj Y
(G, ) ;: If:~.~.
~i
~' ,.I_~_L
~ '"' =It. Y/.{,. ; (~/ ~
t) P jX J/, ~f t ft. r~AJ' 'I J)l; +!X;r M~cL (uA;hj.f.Y )f A'J f(/~ ) tiJ I ' :.:i: V,e.1
(x) •...... ::: J. /f) .  /'~
{ + L 17('1
... e.. I( . e "3 ~  !I;.
X. X ), /:1 if J 2£ 1CXJ :::
f (~) 2r/ 11
__ z :: 0 11 :t .so tltvf + ll +), ::::
0 2l 1. e ') ) ) it;   2+ 8n _ l:t 'f ~ /.Ali ~ . !'f oW,
.5 * r<J l(I'1J] tu i, =. .. y~:i
(hi.' +~ 'I =  .  2 2. Ih f/;., i ~o =   l I
 2  c'1J2n + .. . 'j'; + LI
I
1  =  2 ~K t L  2  1,, c +) i )?  1"...
View
Full Document
 Fall '07
 FOGLER
 Physics, Trigraph, ......, Asymptotic analysis, ) Xlr

Click to edit the document details