quiz3soln - 30% MATH 2930 * Summer 2009 Quiz #3 - June 29,...

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Unformatted text preview: 30% MATH 2930 * Summer 2009 Quiz #3 - June 29, 2009 1. Given the linear differential equation 3;” + y m 333, with complementary solution ya 2 c1 (303$ + 62 sinzr: and particular solution yp = 333, a) Obtain ye by solving the homogeneous linear difi'erential equation 3;: —§— ya: 0; b) Show that yin satisfies y” + y = 33:; c) Show thatbliyand flare linearly independent; and (1) Given the initial values y(0) = 2, and y’(0) = —2, find a solution that satisfies these initial values. (31‘) ("Wt ; o ' 0W \1 CD Wl’ will? air ell-H ‘ O {1; _! fl Ck (1:33 M‘Cz SihK*3X ,‘ {at}: mclgmxiflziofix’ffi wafer“; {q we H C1Z ew'w. 3 f JD 0 V‘- lD) ‘ i; 5 CL -+ gem (:3 l?) \i l" ‘ 3’ *3 kl; t“ G lg‘;§¢ U VFW?" 0" 3“ ‘5‘“ "/ was? ~ :2 gemiif‘l-Jrfilwfil 4. 3 a) {m Kw ‘Smfl (“as l ‘3‘“ 5C “WW Claw: - 0962K l—em‘flz :l 746* 30 to") K} ss‘mc am (Melly Fadtnmwi ’ 2. Find a linear homogeneous constant-coefficient differential equation with the general solution Mas) = (A + Bags?” 4» 083$. m Mm ('mgae?‘ mm a TWM maf- ‘Y‘: 9; f MQ(‘EPHCR‘1Q{.?. (\f— ~15 m it’s/M CQEKXMPHL‘; a yogi Y‘é‘ w> [r ~33 “:5 (wfiCwfl-(rfi‘) 2‘0 {s LMWLWWC 0wa if”? (V1“HV*L{§(W”5)¢ O ...
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quiz3soln - 30% MATH 2930 * Summer 2009 Quiz #3 - June 29,...

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