Question

3. tx" + 2(t-1)x' - 2x = 2, x(0) = 0.

Use the Laplace transform to solve initial value problems

Answer 1

ta" + 2 t. 1) gel-ga=2, a 10) = 0 Take lablace transborn (-2). (s? x(s) +2.L-) (S.XLS)) -5,9XIS)-2 Y15)} => -1 [sºx'+25x] -2[sx'+ x] -95% -2x = } => -sy!-25X-95x'- x -95X-9 X ml-S2-25) -- X ( 45 + 4) = x' (2S+s?) + x(45+ 4) = 2 11 S >> bles AIS+1) X = + 9 2 + 5+2 4 SIS+2) S2 (5+2) 45+ 4 PIS) = SIS+9) 5 Tifoz. vs Plaids.. anes) + 3 Anista) s? (8 +22 i x! 5?1542)2 + x. 4(5+1) S(S+2) = -9 (549) w (544 433 4 482) + X( 453+125+85)=-25- d [xls). (8 4+453+ 4s”)] = -25-4 ds => (54+483 + 45°). XIS) = -5? 45 +C Y10) = Lalo)) = 0 -> CEO S(5+4) - St4) XLS) s² (stg2 S(5+2)2 1 S X15) = St2 (5+3)2 I V alt) = det tet e at