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21d_99f_2e

# 21d_99f_2e - xy dy x 2-y 2 dx = 0(d y 00-3 y 2 y = 2 with...

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Bender Math 21D Second Midterm 11/22/99 Please put your name, ID number, and section number (or time) on your blue book. The first page of your blue book may contain notes. No other paper is allowed. Calculators are NOT allowed. You must show your work to receive credit. 1. (75 pts) Solve each of the following differential equations. If no initial conditions are given, find the general solution. (a) e x + y dy + dx = 0. (b) t dy + ( y - e t ) dt = 0 with y (1) = 1. (c) 2
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Unformatted text preview: xy dy + ( x 2-y 2 ) dx = 0. (d) y 00-3 y + 2 y = 2 with y (0) = 0 and y (0) = 1. (e) y 00-3 y + 2 y = 2 with y (0) = 1 and y (0) = 0. 2. (25 pts) (a) Find the general solution to y 00 ( t ) + ω 2 y ( t ) = 0, where ω is a nonzero constant. (b) One solution to y 00 ( t ) + ω 2 y ( t ) = 0 with y (0) = y (1) = 0 is y ( t ) = 0 for all t . For what nonzero values of ω does the equation have another solution?...
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