Question

y(1/2) = -2, Solve the initial value problem: 9y" + 18y' + 14y = 0, y' (1/2) = -1. Give your answer as y=... . Use x as the independent variable. Answer:

Answer 1

Y CT/2) = -2 qy" +184' +144 = 0 ya Mra) = -1 (90? +180 +14)y=o Auxulary eqution . qm2+18m+ 14 =o ma- -18 + √(1812-4 (147691 2091 -'-18 324-504 -181 180i 18 ma -18+ 6 5 S = -34,178 - 1051 y=et (clos ft x + (2 sings oc) y= ex (a, Cod Jax + Ca sin fra ) y'cx'=-e* (CIALI x + Q Sin F&x) + CD Smusxa ** + GT (453) sy okxis ēr [clicas fox [-1-6] +62 fin špx [-1+ ] Now ychy)= - 2 7 -2= (C,C4 (45) +62 sin 6 x)) -0 y Cava 1 132M ((-37J5) (%) +62 (-3.) for (*

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