Unformatted text preview: , solve the following initial value problem analytically using the method of undetermined coeﬃcients: y 000 ( x ) + 1 2 y 00 ( x ) + y ( x ) = 0 y (0) = y (0) = 0 , y 00 (0) = 1 Notes: You may wish to use numerical expressions for the roots of the characteristic equation just as was done in demo5 in class (and available on the class web site) in order to avoid messy exact expressions. Remember that complex exponentials can be written as sine and cosine functions. Thus, y = e α + iβ ± e α-iβ can be rewritten as 2 e α cos β or 2 e α sin β . (b) Use Mathematica ’s NDSolve to generate a numerical solution to the problem and use this to check your analytical solution (i.e. overlay the plots of both solutions)....
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- Fall '09
- Chemical Engineering, Boundary value problem, Complex number, Department of Chemical Engineering, Mathematica Primer Chapter