ps9[1] - Applied Mathematics E2101y Introduction to Applied...

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Unformatted text preview: Applied Mathematics E2101y Introduction to Applied Mathematics Problem Set #9, due Tuesday, 5 May 2009 All references are to Zill & Cullen (3rd edition). Chapter 3, 3.5: Variation of Parameters 3 21 (Note that both of these problems are perhaps more easily approached by the techniques of 3.4, and the techniques of 3.5 are more powerful and general than we need. However, to keep the analytical manipulation reasonable, we can illustrate Variation of Parameters on these constant- coefficient ODEs.) Chapter 3, 3.6: 3 27 (It is not necessary to graph the solution for full credit.) Chapter 3, 3.8: Harmonic Oscillators 39 40 Supplementary Problem: Sturm-Liouville standard form The concept of exactness, which was discussed for first-order differential equations in 5.6, can be extended to second-order. The equation P ( x ) y 00 + Q ( x ) y + R ( x ) y = 0 ( * ) is said to be exact if it can be written in the form [ P ( x ) y ] + [ f ( x ) y ] = 0 , ( ** ) where f ( x ) is to be determined from...
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