{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW1Key - Due Assignment#1 At the START of tutorial on No...

This preview shows pages 1–9. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Due: Assignment #1 At the START of tutorial on May 18, 2011. No late assignments will be accepted. 1. Find values of m so that the function y 2 arm is a solution of the differential equation m2y” + ny’ — 6y 2 0 for all m > 0. . (a) Verify that the ODE d2y dy w + 3a; has the 2-parameter family of solutions +23; 2 e—z (b) Find the values of c1 and 02 for the initial conditions y(0) = 1 and y’(0) = 0 . Consider the ﬁrst-order ODE (1) (a) Show that y(:1:) = 0x2 satisﬁes (b) Use the Theorem of Existence and Uniqueness to justify the solutions of this ODE for initial value y(:c0) 2 yo. . Find the critical points and draw phase portrait of the autonomous ﬁrst order ODE ill _ dx _ Clasify each point as asymptotically stable, unstable, or semi—stable. By hand7 sketch typical solution curves in the regions in the my plane determined by the graphs of the equilibrium solutions. eytyz — 2y)- . Solve the following initial value problems (a) 3323/ = — x2 + y2 — (mg/)2 with y(1) = 0 (b) (1 + mag—g + 2mg 2 Where with the initial condition y(0) = 0. \$2; ,1,“ ﬂ —1 -7\ I Btu):_(l'1-Cl)e .& ‘+(2)(7~CZ3€’ ’k . , “7-K s .9, <~L+x~tci)~\ 4C1}: ﬂ ’ "K ‘k “a + 3‘6 ‘f LVX s L 31-“ (MN) SJ” -2. ~7¥ ,,\ _‘ ‘ C C 3 1—1 'C e 2;) :Q (-Zfl“? ‘ 1' a ‘? L __ ) .,_ «fix "'1 'l J g C + 11 a f 4‘ 1 Cl \ y) {L “fl? (a, {‘er M /C\o.\ 4/ S "Lt/(Ll \ 6 Par{ [0 3(0)? ‘\ f3 0 -§ C‘ 5r C2 = i ' *- l C = n M) 3%“ O ‘3 1 (he) 2. U CI-f CL :- \ «=3 [1—— Cl )~ CL 17—) ,0“ h’fo <0 Q1- 1C1: C- cl; a & ). FW’ 0* ) H / \QLM) _ ’_ -6 e (i-‘L I.) -cha 1C6, ZK a) g C N “(/an x __«_ - 9. “a S 0/“ 3 2. \blele— ,_,3 le‘Cx)" 1C7” 5 i“. (4/ WM we» WH‘) (Rm Cuwslm‘fm «Ci 41¢ 151;»; a» alum/L r Cgvfoaykﬁﬂb alvk LjLL'ft-bw/ﬁ Ck (/jtfi 0'4}, 50 ’ f” ’ I—TT' O (/Kmftk [JPLU , I a, , w; 7/1144 J 136 v V/06 170.3,- Zﬂn Q, (3-) ) I I F? an lktasJ/J) '3 / 3 v! 2) f 0 ﬂ 3141,, J/ [Law] a)‘\$¢,-£ ’ﬁ . 5° |‘A\(‘J 0A Cc/W cup/Al; 0M ‘ “A ' am/ '1; @me :3“) ‘7 . C - p ‘ ‘fénbé. 6 HM Coat) MW 1“? :3 1m : (\-m> (H32) _______..1 : L____L _.\ l-f m 1, #3 L (Cafu-v\\25 : - _. w .t C L ( - 33. , —— ’1 FL '5 (L f r . / L I ) < l T ) K 5;) 0V1 ‘ we, a J Jw mta 3 WV -3”. _ ‘ ’— : 4 /)L ‘V 7‘ 1 C < /L If: ux. ‘(j - ﬂ 5‘ at C. ' er~ /7, < A ~e V‘ L Q /L “(d4- C (Mp/(,5) ” 4 "/*7\~BC “an “yrs /2 "' 3 < Q at (3ND C r “0.1 7 ‘ S j (:69, mule/1‘1 36- C - (5 L ’ L5 C - n... 1/; : q~-‘ ,'Lﬁ‘11 0/ ‘9 L/-" L. k M‘V‘Cx l“ L“) , 0 ¥ 3 (“ii—‘1’" \$wi: \ & w; \* La -1\ 9L >‘ a}; F) {Lg “(B‘ka Elma/{‘- ‘3‘ 3 1* JW ‘~x(\‘t%z) [41—1 L z e; ;’ ve/ : \‘l’ 1v ‘ 7x (H13) 0 k < \ Z)\ \‘f'hL (l4ﬁ‘ ” l -‘L (HT:) “A >/ |1NL L __ r . . C 1x... g‘ r ‘ l w/L “E C,‘ O \ \6 (1": 7‘ ) :— L .‘7 -— 0 At C‘ *3 Ci 0 (\Avwh/ 172 (/“(MV “3! ‘Ww‘fm’g’ L?“ 0 47k 4\ \1‘}? L SLA\(‘/‘ CW“. ’ .~\ VA d z , 1.),\ a 7L _L..—a K'fP/Z) iii..— \+I;VL \‘V'FL : - LL. '9 Lu?) X.s\ WA" ’M‘L S l L“ s "' " V r a 02’ ('1' =5 ﬂm ’9K S 1‘ X1 1“, \— 1—:1 ’k—djl -i I , _ L)) ,Q.~,~ wk = _L( 4) + C.7,/L-— “’5 b3 ‘H 1% .l-r 1" .L, 2- F.’ ——————-—-’x 0 Q ‘\ 4‘ 11(‘1' 1L.) 9—“) " s “A L ‘ ,1. + 2. 1x. 2 ____,_______._.==ss 2_ (1* Li) ,L/ a éqk 4 \ ,/ (\4’7‘})1 «0 1?: V‘ mz‘ L ‘1’ ( 14>?” ‘ r f "f : ( [A/Lui/ﬂx £3 Yl’i (,thmawb J 79‘ 5-1 (1L. OM {JACK/[Io I {3y Ck Sa' \— 4 a Ca cf "(0 A {L} 1343., \?vr\(; t I :Lffvp. E Mammy b chm" X} “’39) 0Lch Eu 1% a? i ...
View Full Document

{[ snackBarMessage ]}

Page1 / 9

HW1Key - Due Assignment#1 At the START of tutorial on No...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online