Quiz5 - ) + C 2 cos( x ) + e x / 2. Verify that this is...

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MATH 2930 Summer 2009 Quiz 5 NAME: Cornell NetID: 1. Solve the following eigenvalue problem and report all the eigenvalues and all corresponding eigenfunctions. y 00 + λy = 0; y (0) = y (2 π ) , y 0 (0) = y 0 (2 π ) . (1)
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2. Solve the following differential equation by using the method of power series. y 00 + y = e x . (2) Note that by using the techniques learned earlier in the course you can solve the equation to get the solution as y ( x ) = C 1 sin( x
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Unformatted text preview: ) + C 2 cos( x ) + e x / 2. Verify that this is indeed the solution to the given problem. Now try to match your power series solution to given solution. Does it match? If not, then how do you explain the apparent paradox? You may use the following: sin( x ) = x-x 3 / 3! + x 5 / 5!-. . . , cos( x ) = 1-x 2 / 2! + x 4 / 4!-. . . , e x = 1 + x + x 2 + . . . . 2...
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This note was uploaded on 01/21/2011 for the course MATH 2930 taught by Professor Terrell,r during the Spring '07 term at Cornell University (Engineering School).

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Quiz5 - ) + C 2 cos( x ) + e x / 2. Verify that this is...

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