Unformatted text preview: The generalization of the Wronskian is given on page 221. It is used as in the last Chapter to show the linear independence of functions, and in particular homogeneous solutions. • For the situation where there are constant coefficients, you should be able to derive the characteristic polynomial, and the characteristic equation, in this case each of n th order. Depending upon the types of roots you get to this equation, you will have solution sets containing function similar to those in the second order case. (Examples 24, p. 227229) • The general solution of the nonhomogeneous problem easily extends to the n th order case. (Equation 9, p. 225) • Both variation of parameters, and the method of undetermined coefficients generalize to determine particular solutions in the higher dimensional situation. (Example 3, p. 234; Example 1, p. 239) Relevant Applications: • Double and multiple spring mass systems...
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 Spring '10
 DorothyWallace
 Differential Equations, Linear Equations, Equations, Derivative, Higher Order Linear, Order Linear ODE

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