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Unformatted text preview: its general solution. y (8) + 4 y (6) + 4 y (4) = 0 EXAMPLE. For each of the following functions, write a diﬀerential operator L such that L [ y ] = 0 has the given function among its solutions. 1. e 5 t 2. t 2 e 9 t 3. e 5 t cos(7 t ) EXAMPLE. Find the general solution of y (6) + 64 y = 0 . Hmmm. We have a problem. We need all six sixth roots of-64. Here’s how to ﬁnd them. HOMEWORK: SECTION 4.2...
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