# RAT2 - x 10 x = 20 x(0 = 5 ˙ x(0 = 3 5¨ x 20 ˙ x 20 x =...

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ME360 - Dynamic Systems Prof. Gillespie - Fall 2010 RAT 2 - Due Sept 21 due at 12:50pm Name : ................................................... For each of the following diﬀerential equations, ﬁnd the characteristic roots and write them in the box. Then choose the solution from the list below. Each equation has a solution, but not all solutions match one of the equations. Hint : You will not have time to solve all of the equations or even diﬀerentiate and plug in. Use the characteristic roots and initial values to guide your choice of solution. Diﬀerential Initial Characteristic Solution equation conditions roots number ¨ x + 7
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Unformatted text preview: x + 10 x = 20 x (0) = 5 ˙ x (0) = 3 5¨ x + 20 ˙ x + 20 x = 28 x (0) = 5 ˙ x (0) = 8 ¨ x + 3 ˙ x + 2 x = 6 x (0) = 3 ˙ x (0) = 4 ¨ x + 16 x = 144 x (0) = 5 ˙ x (0) = 12 Solutions a) x ( t ) = 1 . 4 + 3 . 6 e 2 t + 15 . 2 te 2 t b) x ( t ) = 1 . 4 + 3 . 6 e-2 t + 15 . 2 te-2 t c) x ( t ) = 4 sin 4 t + 3 cos 4 t d) x ( t ) = 9 + 3 sin4 t-4 cos4 t e) x ( t ) = 3 e-2 t + e-5 t f) x ( t ) = 2 + 6 e-2 t-3 e-5 t g) x ( t ) = 3 + 4 e-t-4 e-2 t h) x ( t ) = 5 + 4 e-t-4 e-2 t i) x ( t ) = 8 e-7 t cos 2 t + 2 e-7 t sin 2 t j) x ( t ) = 8 e-7 t cos 3 t + 2 e-7 t sin 3 t Page 1 of 1...
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