Question

Im sorry I really had to repost these 2 questions, because I really couldn't understand any thing from the handwriting as it was not clear.

thank you very much for your time

3. Find the inverse Laplace transforms: (a) e-{_5)} (1) c-'*:*}(0) "{G+236 +16}. 4. Use the Laplace transform to solve the initial value problem y' + 4y = e34 subject to y(0) = 1, for y(x).

Answer 1

* - # ouis -6 -(R) - ܕ ( ܟ)-( - 6 ܕ(@)-- -()- -(P) ܠܦ ܢ * -[e},-. - - :2 n.

| : ਜੈਕ + 9 ਚ} = { 9 { } : Cost) + 9x Sing+ Since List " = Cascat) = Siਅ (4) = s3+) +3 Sing+) .

S2 (( S ) - 2 S)(s+16) ( s42) (s(6) । ' ਚ - ਮਾਂ | = ਫੇਰ | ਜਨ}* 5 } ਕਵਿਜ਼ -- ਵਜਾ ਛੋਕਰ-34 ) 3-% = ਸ਼ਾਦ - 4 S (+) - +s (4) S S+2

Swe cਤੋਂ 4SH (+) 525-ajte at Elektrons = cos cars. 4. The differential equation is - y'+4y= ex with y(o)=1 - Applying Laplace transformation 1(8') +44(0) = 4(238) [s (4) - ) + L = => SL(*)-1 +44(X) = 5 + 6+4).[13) = 35+1

: ੪%) = ੬%e4% h + S | + 24-F-1)+ + = *+-+ : - - (1)+5+5). 5) = (+5.(1* * * & * + +2 - - S, F3 = 7 4 [ sRI ,
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