MATH 3008 Midterm: Exam-MATH3008-2005April
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D u r a t i o n : 3 h o u r s. Students must count the number of pages in this examination question paper before beginning to write, and report any discrepancy to a proctor. This question paper may be taken from the examination room. This examination may be released to the library: (a) state picard"s eristence and uniqueness theorem for the initial-value problem. A " : f ( r , a ) , a@ o ) : a o . 2 r " g " + ( r 2 - r ) a " + 9 : 0 . (a) find two (nonzero) iinearly independent solutions valid near r0 : 0. [14 marks] (b) express one of the two solutions as an elementary function. [2 marks: (a) find the general solution of. , 2 a " + s r y " + 6 a : 0 f o r n 1 0 .
