Question

to solve the use the laplace transform following initial value problem olt 23 yllty 3 Lt 이 y codzo, y'Co=2 solve for r= yCV)

Answer 1

Date Page soin given that yllty = <l <3 {! t73 y lol 0, yllo) = 2 2 tula Laplace both side abone {yltyy = Y! oste 3 t> 3 L&f(t)} where tuke fit= octub t>] -t then ff (117= fit? dt Irmula -st е -st T fit? dt & fe fltidt ſo est I at t -st 3 est. lt 1) 3 -38 - laat s U f W} le-35

Page also we know the Formula 4y"): sky - syco- flea) & Llyga LXgg2 y above becomes (1) 17"+ {y} = 1446) by linear property -38 - e 8 sy - 846) -yr-) +7 t (8²+1) -38 sly .8.0 2 L-e - 2 = - 34 & - é 38 s +2 1 341 ar y I-e-36 2 & (shell 841 take inverse laplon both siche egy = L / Ine-31 81841) 2 8241 Use linear property of diverse laplan

y 녘 Iné v e s(821) 8201 -35 y { score try chemi + 2L1 ? Blool -38 2017 Scarell 244 Bel s(861) е to evaluate 17 we use the second shitting property Inverse lap lace transform which it $(821) of { font Eltal tla where FA)= 'L {festy to here we need first t" { scrie SCARI) ) L" y sister) } } , 1} (by pochial t" { 1 } - LA Fraction $

Page SOD of 1-1 cha Sinat 8pa cos at میر get FLA) 223 El sales & alle3 ceived take 1- cost 1-cosit-3) t> = G(A) th] (take) then (1) beames y = I-cost - alt + 2 sint y = l-cost & zsint & Git) is the solution where alt) I-coxlt-3) t> tc