Question

Solve: y' – 4y' + 3y = 9t – 3 y(0) = 3, y'(0) = 13 y(t) = Preview

Answer 1

Given DE, y"-4y+3y=9t-3° 4 (0) = 3, y 10) = 13. Apply LoT on both 0 sides. hy" - ugl+34} = (49t-3} L241} -4224} + 3 L2 y} = 944+3 - 123}, s yes) - S410) -y'60) -4 ( 85(s)-401] + 37(s) = 96523 5*96) – 5•(3) 403) -4 (990) –3] +394) = S- s965) -35 -13 -45605) +12 + 3515) - 9-3 S gos) [s=_45+3] -35+1 = 962 S2 52 s 9 5 (5) { 5² -4 s +3] = 18-33 +35+1 982 yes) (52-43 + 3) = -35+ (3. yes2 = 9-35 (351) 8 (5-us+3) (3243+3) Jes) = (9-3s) et 82135+1) sr 18²_uJ+3) Apply énuese Laplane transform en both sides as + 5² (35+1) 7 1 82 (stus+3) S T'{ 9-35+353 +522 s² (32-ust

353+52-93+9 - A + * + Šat 5-3 st szt + D S2 5² (34) (5-3) 353 +5²-gst s cs_12153) TOSES) As. (S-1) (5-3) & B (S4) (-3) + C CS-3).32 ses 37 ts-g5+ 9 = AS(SA) (3-3) + B (S-1) (5-3) + ((S-305 to S2000 SO put s=o in en 3 we get vele for 8' oto-o+9 = A (0) + B (0-1) (0-3) toto 9=387) B-) => 183] Put S=IWA GM 6 we get vale for c' 303 tout -9 (0) + 9 = A(0) + B (o) te + 9 = A(0) + B (o) + c(1-3) (1) + bco) P = otot c(-2) (1) to

10 =-26 > C= -185 » [[= -5] put S= 3 in a ③ we get vale for "D" 3 (3)3 + (3) 2 _ 3 (8) +9 = to 8o (CO) to (3² (3-1) 81+94 +9 = 0 toto + 0(9) (+2) forula? 90= +180 4 + 3 = eat D=805 ų + z = t ed t3zl. g3 terry Comparing on- both sides 3 = Arcto 3= A-8+8 ..Cars, Dar quo sub A, B, C, D vales in S² (51) CJ-3) sman (2) " 33²+32-35+92 eth ý (13) g = 2 88-) (3-3)) YH) = [ { 32 th 3 3 - 2 15th 5+3) lylt) = 3-(1) + 3-t - set 45.83t| 1 werifuti Tylt) = 3+37 + 5 est-se Y10)= 3totoest 40)=3 400- 8+3+15- 5 - 13/

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