Section 6
1e 3x cos4x+ c 2e 3x sin4x = e 3x(c 1 cos4x+ c 2 sin4x): 10. The auxiliary equation is P(r) = r2 6r + 34 = 0, with roots r = 3 5i. Consequently, two linearly independent solutions to the di erential equation are y 1(x) = e3x cos5x; y 2(x) = e3x sin5x; so that the general solution is y(x) = c 1e3x cos5x+ c 2e3x sin5x = e3x(c 1 cos5x+ c 2 sin5x): 11. ................
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