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Unformatted text preview: MATH 152 L1 & L2 Applied Linear Algebra and Differential Equations Spring 2004-05 ¥ Week 04 Worksheet (February 21, 2005) : Second-Order Linear Equations Q1. (Linear property for second-order linear differential equations) (a) If y 1 ( t ) and y 2 ( t ) are two solutions of the linear homogeneous equation y 00 + cos ty = 0, and a 1 , a 2 are arbitrary constants then show the linear combination a 1 y 1 ( t ) + a 2 y 2 ( t ) is also a solution. (b) If y 1 ( t ) is a solution of the linear nonhomogeneous equation y 00 +cos ty = 1 and y 2 ( t ) is a solution of the linear nonhomogeneous equation y 00 + cos ty = t , find a linear combination of y 1 and y 2 which is a solution of the linear nonhomogeneous equation y 00 + cos ty = 3- 2 t . Q2. (Homogeneous equations with real constant coefficients) Consider the second-order linear homogeneous differential equation 6 y 00 + 5 y- 4 y = 0. (a) Find two (linearly independent) solutions of the equation by determining the two (distinct) roots of the characteristic equation.of the characteristic equation....
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