Question

(1 point) Transform the differential equation -87 5y" +42y" - 5y' - 42y = 2e y(0) = 0 VO) = 0 y"(0) = 1 into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y, (not Y(s)) Therefore 1+ 3+1 *+8 Taking the inverse Laplace transform we get y

Answer 1

Solution : 0 gy" de & Given that The differental Equalor 42.3"-sy'.uay" joo)-o ' yºu:0 : j'(0 : 1 Taking haplocc Toanscom on both side's get 5[ 849)-gʻxo- syconf'cov] +42[p?ych - citozytos] wc - 3 [oyco)-4101] -42 715) - 378 53yco) -5 +433365) - 53c9) - 42945) {5374802-33-42]70)- : [sºc Jórua)-153742)] C5) = 2 tó 0+ 8 5+8 [159742)(8211465) = 2+53+40 3+8 ( 53742)(3-1) 7(9): 33742 078 Y13) : 53742 [.2?5?ca=bla-be] (5+8)(554422 000 - 405): 10+8)(0+1(0-1)

witing partial reactions A 3 + (3+8X9+10-1 (0-1) B 13717 578 1 : A0071) (978)* 310-100+8)+6(371)63-1). 3:1 1 = A(2719) A: 1 18 3-4 B1-2)7) 13:1 u 0:-8 1:618+1)18-1 :917) - C 65 63 1 ly: to bi ju ári gre Taking the invecic kaplace Toanifoom se get byees -t -87 et 18 14 63 X

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