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This is equation 8: ya(t) = n(e) / 102 .

Use Equation (8) above or go through the reductio-of-order process to find a second solution 72 of the preceding equation sucSolve the initial-value problem y(t) + 4y(t) + 13y(t) =0, y(0) = 3, y(O) = 6. Express you answer in the form y(t) = RettcoVia the substitution y = tm , where m is a constant, find two, linearly independent solutions Y1 = tmi and Y2 = tm2 of tº y


full question, which contains y1
Show by substitution that yı - et is a solution of y - (1+1)y + 4y = 0 on (0,-). Use Equation (8) above or go through the re
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Answer #1

ON Y = et Y-(1+1) 9 + ty=0 on (0,07 som given Ret) – (1 tel. 11t = Tilt Tilt I I ē è Spibat (52 - de ylt) 2 et 5-(1+tlat ce( +4 6 +137 W) = 0 410)3 4 10 6 Auxiliary equation is m + am +13 - 0 ma – 4t 116-1349 2-1+116-52 = -9+ 5-36 =-946 = –2t3i YH(3t-5 y (4) = ē+ ( 3.60534 + 4 sinat) = ( 3cosst + sinat) - e cos (32-5?)). Fest (coscoe - Sams). B Time-vasing amplitude is

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