notes 4-2 - its general solution y(8 4 y(6 4 y(4 = 0...

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SECTION 4.2 Nth ORDER CONSTANT COEFFICIENT STUFF Everything works the same as in the second order case, except it may be a lot harder to find the roots of the characteristic equation. Also, a root may be repeated several times, in which case multiply by t , then t 2 , and so on, so that you get the necessary number of solutions, which for an n th order equation is n . EXAMPLE. Use the D -operator to rewrite the following differential equation, then find
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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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notes 4-2 - its general solution y(8 4 y(6 4 y(4 = 0...

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