4038HW12_Su2010 - r that works, you will need a second...

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Homework #12 to Hand In Math 4038 Summer 2010 Print Your Name: S how all work: We can give credit only for what you write! Hand in only your own work—nothing copied! Please do not convert exact answers into decimal approximations. Please write neatly so that the grader can read your work easily. You may print a copy of this Fle and write on it, or use a blank paper with your name at the top. The maximum score possible is 10. Question. Consider the Cauchy-Euler equation x 2 y 0 - 9 xy 0 +25 y =0 (1) a . Find a solution of the form y 1 ( x )= x r to Equation (1). b . If you ±nd that there is only one value of
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Unformatted text preview: r that works, you will need a second solution y 2 ( x ) that is linearly independent of the ±rst. This can be done by the following Method of Reduction of Order: Substitute y 2 ( x ) = y 1 ( x ) u ( x ) into Equation (1), do the di²erentiations and note that several terms cancel out . Now substitute v = u into the resulting equation after the cancelations, and you will obtain a ±rst order equation for v . Solve for v and then integrate to ±nd u ! 1...
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This note was uploaded on 01/06/2012 for the course MATH 4038 taught by Professor Staff during the Summer '08 term at LSU.

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