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Unformatted text preview: MAD 4401 Quiz 5 James Keesling 1 Linear Ordinary Differential Equations Problem 1.1. Let dx dt = A ยท x be a differential equation where x ( t ) = x 1 ( t ) x 2 ( t ) . . . x n ( t ) is the solution being sought and A is an n ร n matrix with constant coefficients. Prove that the following formula gives a solution to the differential equation. x ( t ) = exp( t ยท A ) ยท C 1 C 2 . . . C n Problem 1.2. Suppose that P,D and A are n ร n matrices. Suppose also that P is a non-singular matrix and that A = PDP- 1 . Show that exp( t ยท A ) = P exp( t ยท D ) P- 1 . Problem 1.3. Suppose that D is a diagonal matrix. D = d 1 ยทยทยท d 2 ยทยทยท . . . . . . . . . ยทยทยท d n Show that exp( t ยท D ) = e d 1 t ยทยทยท e d 2 t ยทยทยท . . . . . . . . . ยทยทยท e d n t 1 Problem 1.4. Solve the following differential equation....
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This note was uploaded on 11/12/2011 for the course STA 3032 taught by Professor Kyung during the Summer '08 term at University of Florida.
- Summer '08