# notes 10-1 - 1. y 00 + 4 y = cos x, y (0) = 0 , y ( ) = 0...

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SECTION 10.1 TWO-POINT BOUNDARY VALUE PROBLEMS A typical two-point boundary value problem consists of a diﬀerential equation y 00 + p ( x ) y 0 + q ( x ) y = g ( x ) together with boundary conditions y ( α ) = y 0 and y ( β ) = y 1 . Contrary to initial value problems, such boundary value problems may have no solution at all, a unique solution, or inﬁnitely many solutions. The boundary conditions may involve y 0 at one or more points instead of y . EXAMPLES. Solve the given boundary value problem or show that it has no solution.

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Unformatted text preview: 1. y 00 + 4 y = cos x, y (0) = 0 , y ( ) = 0 2. y 00 + 4 y = sin x, y (0) = 0 , y ( ) = 0 EXAMPLES. Find the eigenvalues and eigenfunctions of the given boundary value prob-lems. Assume that all eigenvalues are real. 1. y 00 + y = 0 , y (0) = 0 , y ( L ) = 0 HOMEWORK: SECTION 10.1 2. (if time) x 2 y 00-xy + y = 0 , y (1) = 0 , y ( L ) = 0 , where L > 1...
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## This note was uploaded on 11/28/2010 for the course M 56840 taught by Professor Schurle during the Spring '10 term at University of Texas at Austin.

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notes 10-1 - 1. y 00 + 4 y = cos x, y (0) = 0 , y ( ) = 0...

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