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05m2-solution

# 05m2-solution - Math 5A Midterm 2 Spring 2005 Instructor Gt...

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Unformatted text preview: Math 5A Midterm # 2 Spring 2005 May 20, 2005 Instructor: Gt Wei Name W Discussion time (circle one): 8am ; 5pm; 613m; 7pm Your Scores: 1. ‘. 2. ....... M 3. ...... n 4. ....... ‘. 5. . ,,,,,, H Your Total Ali questions have equal points, Continue on the back of the page if you need more space. Good luck! 1. a) Find the general solution of yr: + 4y! + m 81:? b) Consider the diﬁetential equation y” + ay’ + 4y m 0, For what values of a will the soéution osciilate? 5|} y(/‘%‘Fg"f€fg-:0 I JL%‘fP‘f\$L;0 [zﬁﬂl ._. H— g“ :61 6 yr;- MW Bffc , 492mm; 9”- lf+€1f€.’ 2/1 + WWHWB) + WNW/Hm} : ff" W438 , M+wsao f 2/1 jay/3+“ M 2. Solve the following initial value problem m” + 5:1: = cosh/5t), 32(0) = 0, m’(8) w 7’4; ﬁamj/mes eff/«2 X'”+r,\» : 0 riff—\$0 , Y==Eﬂf XL :que + (2. {[uﬁ’f XI, :- 1f[/—) Mfff + x3 mﬂ) Xr' :2 {A mﬂf + r; Sin/Ff) + f (-— ﬂ'ﬁWnﬁf H613 4432+) XI," 2: 2 («f/4 mm +ﬁ/3MJH) + H» 47-) mm‘ «475 mm) xr’ww s: 2{.«J?/+ Ina/ft +ﬁx214m) :: 44qu , ' m "ml" A'ﬁo / W/ a”? m) “w: 5’ Mfﬂ' + 4» Wﬁf + f 1‘ mﬁf 3—3" 34 Write the differentiai equation :E"+2:c’+2:-~m2=0 into a system of ﬁrst OI‘dGI differential equations. Then determine the equilibrium solutions of this system Leif; yﬁxr y/JFZJ I 7A». jar—5+ W QM“. pf; 53/ = g! VIM“ (cg/Luff 9’; W 4. Find all the eigenvalues and an eigenvector of the largest eigenvalue. (12 2) A: 2 0 3 2 3 0 (MA 2 2 .«X1 .7: 1 {/3 / 2 “A 3 :, (l~/\)(/\~7)-~2(~22\~5) Z 3 vi +;(6+2,\) :(/*A)U1”7)+(f{/{43)4 MW) 5 ’g I “I, C 13a+§)[(].../\)Uw;).f:é;) \$0+5)(~4"+M+s~) : “0+5) *6) (AH) 4:: 0 w 2 2: ' “22 ( I by ( , / 2. VS 3' “"3 0 “F 2 3 w? 0 “y “'3 f f "21/, +VL+U3 no _—’——3 l? “I i ; “V1, “('V; :0 I? 0 0 5. For the system of equations 33’1 \$1 -— 22:2, 3:; x1 + 4.732, M if (a) Find the generai solution. (b) Find the soiution satisfying the initial conciitions 391(0) 2 4, 932(0) = 2. a” {if (I "(f/{U ...
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05m2-solution - Math 5A Midterm 2 Spring 2005 Instructor Gt...

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