Question

solve differential equation thru laplace transfrom and inverse laplace

dx + 2 d.²x - dx = 2X= 4 + et dt' at² dt

with complete solution

Answer 1

Am) Given differential Equation is dex dt3 +2.138 dx • 26 2x ute df2 df Take Lapalace Transferm 83x(s) + 25% x(s) - S x(s) – 2x(s) colf 'S-2) (53 +252-5-2) x (5) us-8 ts S(5-2) X (5) 55-8 515-2) ( 53 +252-5-2) As, 33 +252-5-2 - (3-1) (5+1) ( 5+2) So, x(s) 55-8 5(5-2) (5-1) (5+1) (5+2) x(s) A S + B + + D 드 S-l اه + S-2 STI E $+2

Go) AE syls 1. SSD A = (sxo) - 8 은 -2 2 (0) (0) () (아 B- (S-D (s) S-2. 0 - S2 -8 10-8 -) 12. Q (2) [21)(2) 2X3M c. (9) 79 11 t3 Sx) - 8 11-2) (+))(142) 58 TX2X3 는 6 - C: 2. ( SD X(s) 'Se) SYCH) - 8 -13 13 6. (D(I) () (-142) 3 × (-2)

E = (S+2) (5) \ 'S=-2 81- 낸 S아) -8 (-)(--) (-2) (24) 8x3 TD - 3 So, A - -2, 33 능 C=) 2 D 13 - , 1 0 9 E- E = -3 So, X(s) 13 + 도 \ + 12 (S-2) 2 (s-1) 6 (SI) (+2) Taking Invern Lapalice M(4) - -2 + e2 & t +13 3 3e~24 12 드 6 니 A70
Solution is provided in uploaded pics.

If I helped you then Support me with a Thumps up