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Midterm 2 Solutions

# Why this is so ill explain in the class 6 solve the

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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 r-lJh-A'J., "j-n/ /-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;h-j.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£ 1-CXJ -::: f (~) -2r/ 11 __ z :: 0 1-1- :t .so tltvf + l-l +), :::: 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"...
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