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1. (a) x,= c,2' + c24' (b) = c,4' + C2r4' (c) x, = c^costfr + C2Vysindr, where cosO = -V3/3 and sing = V6/3. (d) = C,(2/3)'/2 cosjrr/2 + C2(2/3),/2 sin;rr/2 +4/5

3. (a) Y; = b/{ 1 - a) (b) m2 - a (1 + c)m + ac = 0. Two different real roots, a multiple real root, or two complex roots according asa(l+c)2-4c>0. = 0, or < 0.

5. If a # -2, then D = c/(a + 2). If a = -2, then D = c/(a + 4) = \_c. 7. (a) Stable, (b) Not stable, (c) Stable, (d) Not stable. a(\+gy

9. (a) Y* — —--T——----(when the denominator is not ^ 0).

Damped oscillations when k < 1. 11. (a) ofi < 4or(l - a) (b) ap < 4a and a < 1.

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