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wksheet3soln - Sol[0 MATH 2930 Summer 2009 Worksheet for...

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Unformatted text preview: Sol [0 MATH 2930, Summer 2009 Worksheet for Week 3: Homogeneous Linear Differential Equations 1. Verify that y1 = 3‘50 and y2 2 we”, are linearly independent solutions to the differential equation 3;” + Zy’ ~§~ y = 0. Then use the initial conditions y(0) = 2 and y’(0) = ——1 to find a particular solution of the form 3; = 0:111 4- C2y2- 5%) Sallie-37 IM E, L '5 WM 0n 0} .M-a—M“ \k‘: "5 a!“ ~V~ ‘u “it v “Q“ i: \l‘ l 6 «WW w abetfl wow” 1;“ ‘K “‘6 u_ . ’l( -y_ ac ”I?“ “a 432*}?1,“ $475 “ewe, 3 X f2,» K“ afiffi . ”1- i ‘1'- “K ‘ w WWW t, 45* 1K ”tweak/I” «t leebfil’em 195 Lek mm? A 63$ 9-) \ 7< {an a.) 15. ”7% 74 (‘3 \ M It 2. If the roots to the characteristic equation for a homogeneous linear differential equation are 2, 1, 5i6i, 3, 2, ifii, and Sim, write the general solution to the differential equation. - W i (@m ) mi [,9 Mia “M3 {mi Caw-Hékaia‘w‘ 40 Kit?) gel“; Gama“ Céex _ _ i fig "1,3 £75“ {153% gm“) + Kit-6% (:ng £1.73 59W? in; ‘3‘“ (4*) C3 9,?” 7t . 5’“ {BK 2U. 63¢ 1’ “15% [WW (9M Lg“) g A [93% + m5“ [C69 4m Qw- {2} “SM {90 '1‘ C3?“ m Cu?) + [1“ E Jr (Cg or» 5“ “i Cm 5““ (9K) Wmmmmwm.wrmig : wwwflW . M ...
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