Unformatted text preview: EXERCISES 4.6: Variation of Parameters, page 197 1. The auxiliary equation in this problem is r 2 + 4 = 0, which has the roots r = ± 2 i . Therefore, y 1 ( t ) = cos 2 t and y 2 ( t ) = sin 2 t are two linearly independent solutions, and a general solution to the corresponding homogeneous equation is given by y h ( t ) = c 1 cos 2 t + c 2 sin 2 t. Using the variation of parameters method, we look for a particular solution to the original nonhomogeneous equation of the form y p ( t ) = v 1 ( t ) y 1 ( t ) + v 2 ( t ) y 2 ( t ) = v 1 ( t ) cos 2 t + v 2 ( t ) sin 2 t. 211...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Cos, Boundary value problem, ORDINARY DIFFERENTIAL EQUATIONS, Boundary conditions, boundary condition

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