4038HW17_Su2010 - y = ( x ) c 1 J ( ( x ) ) + c 2 Y ( ( x )...

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Homework #17 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. Transform the diFerential equation y 0 + x 2 y =0 (1) into a Bessel equation of order ν , so that you can write the general solution in the form
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Unformatted text preview: y = ( x ) c 1 J ( ( x ) ) + c 2 Y ( ( x ) ) You will need to nd the correct value for and the correct functions ( x ) and ( x ). (Hint: Note that y and y in (1) represent derivatives of y with respect to x . Let y = u x and z = 1 2 x 2 and use the Chain Rule to convert to an equation using derivatives of u with respect to z . Here J and Y are Bessel functions of the rst and second kind, respectively.) 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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