Question

Solve the initial value problem below using the method of Laplace transforms. 4ty'' - 6ty' + 6y = 36, y(0) = 6, y'(0) = -1 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. y(t) =

Answer 1

Q = 36 co solve by laplace transform uty" - 6t y' + by with yo) = 6, ylo) = -1 som we know that Lly'll } s Y(8) - 6 s Lights y (0) © L {p" (4) 3 s ylo) – y'60) Il s² Liyus-sy(0) 3) .? s 78) 68 ti il G L (il il Ś also S L {{ $(!)} = d (L4f4037 ds => [- 48²4 + 68 ) Y'18) +688 +12). Y18) Il 24 solo => -28 ( 25-3) y'ls) + +(-2)(2) 428-3) yls) 12. (3 E 3-2 28

a =) y'(x) + 2 Y(x) = ogla 2 I order diff eyn which is linean its IF alns e e I 11 2 = is tha soll of 6 6 کرلے + c IF = IF. (3) قیم s 2 ds + c s -> = Y(3) os dos 2 y(8) = 6s + c S С => Y(8) + ul olar 2 S ~ L applying an transform

required soim. is which S 6 -t (P) h then from o = C => y'lo) = 1- o + c So y' (O) put world (7) h 7 + 9 8 = = 171R (1) 2 cit then out the J つくば w? 3 we know that 2 0 1 2 € Tufo t y(t) AL f. ->