sol4 - c 1 + c 2-12 =-4 c 1 + 2 c 2 . Solving the system we...

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MAP 2302 Fall-2011 SOLUTIONS: Section 0100 Quiz 4 1. Solve the initial value problem y 00 + 2 y 0 - 8 y = 0 y (0) = 3 y 0 (0) = - 12 . SOLUTION. The characteristic equation is r 2 + 2 r - 8 = 0 . It has the roots r 1 , 2 = - 2 ± 4+32 2 , that is r 1 = - 4 and r 2 = 2. The general solution is y = c 1 e - 4 t + c 2 e 2 t . It’s derivative is y 0 = - 4 c 1 e - 4 t + 2 c 2 e 2 t . The initial conditions give the system of equations 3 =
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Unformatted text preview: c 1 + c 2-12 =-4 c 1 + 2 c 2 . Solving the system we obtain that c 1 = 3 and c 2 = 0. Thus, the answer is y = 3 e-4 t . 2. Are the functions y 1 ( t ) = cos t sin t and y 2 ( t ) = sin 2 t liniearly dependent? SOLUTION. Yes, the are: y 2 ( t ) = 2 y 1 ( t ). 1...
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