Question

Entered Answer Preview Result [e^(-2*1)]*[8*cos((9/5)*1)-14*sin((9/5)*t)] - * (cos(.) – 14 sin(6-)) incorrect The answer above is NOT correct. (1 point) Find y as a function of t if 25y" + 100y + 181y = 0, y(1) = 8, y'(1) = 2. y= e^(-2*t) * (8*cos(9/5*t) -14*sin(9/5*t))

Answer 1

Mere the given differential Palio 25 1009 1814 +0 - Go to auxilaley 09 9 2574 1000 18O m: -100 100)? (9 (181) | 2 195 -100 + 10000 - 100X181 50 = -100 + 10000 - 18.00 50 -100 9100 50 go. -100 50 m = - 2 9 ; which is complea roolo So, genere bolletion to the given differential 09" is 964) - 2 24 (41609(24) + Cool ( 34)) le yu) - ēpt (4coo( ?!} + Co.bin (94) — differential wirito. t ( with rex poctive to t) y'ut) = -2724 ( 41100 (95) + 6961† ( 94,)) +2 9+ (-213( 94 ) +60 600 (X)) yC -2014 ( 106 (24)+(910 (94) +20 (-9.9. ow (94)+ gacob (94) 50g put t=1, in ear we get yx =1) - ē° ( 41606 )+(26ri ( .)) 1 = 2 ( 9100(%)+(251(3) (0)=1 Similarly pul t-, in om? I we got ( =)) = -2 2 ( x 6( 2) , Đồ (2) + ( 21 n (2) 29 (op(40)

15-22(906(3) +(25\)) + ē ( 13.40€) + 952.600(3) 1==3(1) tē% (-39.5) (2) + 949.606()) — ( 22 (105(9) 4 2010 (9) = 1 ) #= ? (4100(?) + 902 cod 73). from can 9. 43 gecon(3 + gre?) solvurig og fo multiplying eq? © by q additing in'cq? ☺ og galécol) – 96oeoin ( ) + += neºcari ()+ game 2206 (*) Şth - Eyon (1) – 2 69.2013) = cein (3) - I.c2ec00(%) 4 (0.00425) +en (0:1953) — -112 9 (0.09225) + (3 (1,2177) — then eqh y become so (0.1953) + ((0.00425) after solving caq? @ Po vegets 1=7.684684 03-9,2727-9 a=8 q log= 90 then put this values in egno , ean becomes 944) - fot ( 9106 ( 9 ) + (ga Join) (9)) yu) = {2+ ( 7600 (94) –gyon ()) which is required general boll to the given different feel aap? e 25y +10oy!

multiply eq? by 011959 2 cqn u by 0.03925 vegety and add 0.1958 (-112 4 10.03825) + c2 (112177)) = -1,4989 = 0.0051754 + C2 (0:1649) 0.09825 ( 1 = (110.1959) + 62 (0-00425)) = 0.09825 = 0.0051754 + 0.000)62542 + -1.52655 - 0.16468502 C2 = -1.52655 - 164695 -9 (23-9.2723 put con= -9.27ins in eg? , we get 12 4 (0,1359) +012 (+0.00425) 1 - 4 (0.1969) — 0.0994 cq 1.0394 0.1359 = 7.684 N 8
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