Question

I posted this problem before and the answer was incorrect, so please can an expert with great knowledge help me this time.

(25) 4. Find the solution to the given system that satisfies the given initial c [1 0 -17 X' = 0 2 0 X(t), X(0) = [1 0 1

Answer 1

X X(0) x lt) 2 2 0 Let becomes thon -bc (0) -2 21 21 22 - TovinLoploctranfarm in beth Side uotion the abovs Sx(s-o) = Xls -(s) sy(s) 2Y(s) Sz(s) - Z(0) xs) Zs) sy(s - 2 2Y(S) (21 x (s (2 From (2) (s-2)(5) Y (S) = S-2 Toving inverse Loploce trondorm osorm. bolh side we 2c From Z(s) Substitut ing voue 3 -zis) in (3) we (5-11-) x(5) 23 =X(s 2s-1)=0

or, x(S = 2. (s-) (s-) Tovina inverse Loploce transform brih side , Sinht 2さCosht - From (3) oe S-1)) Substitutiog volue x) in 2 (S-1) + 2 2 inyerso loploe transtorm beth Side, Cesht Taving 2Siaht 2Cochit Sinhtt ) Xit) Cosa2siah|t Henca the Kaired Selution is, 2eCash Sink (t) x t 2 2t Cosht2 Sinhl4)|
N.B.
sinh(t), cosh(t)
are hyperbolic function .

If you have any doubt or need more clarification at any step please comment.