Given two differential equations: + 2x = Y dt2 + 2y = x dt? where a(0) = 4, ' (0) = 0, 3(0) = 2 and y' (0) = 0 (a) Solve the simultaneous differential equations using Laplace transform showing that 483+10s X(s) = (s²+1)(s²+3) and 283+88 Y(s) = +1)(s²+3) (b) Hence, using the inverse Laplace transform find æ (t) and 3(t).

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