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Unformatted text preview: Differential Equations final exam Friday, June 17, 2005 please show all your work to get full credit for each problem 1 . Given the initial value problem ( x 2)( x + 3) y 00 + 2 xy + 4 y = ln( x + 1) and y (0) = 8 and y (0) = 2 ( a ) For which values of x is a continuous solution guaranteed to exist? ( b ) For which values of x will a power series solution X k =0 a k x k converge? 2 . Is the pair of functions { f ( t ) = sin t , g ( t ) = t 2 sin t } a linearly independent set? 3 . Find the real part of the complexvalued function (3 i ) e ( 4+5 i ) t . 4 . Given the initial value problem dy dx = x + 1 y and y (1) = 2 ( a ) Complete the first couple of iterations of Eulers method with step size x = 0 . 1 by completing the table: x y dy dx approximate y 1 2 1.1 ( b ) Rewrite the differential equation and initial condition in terms of one integral equation. 5 . Sketch the direction field and a few representative solution curves for the differential equation dy dx = y ( y...
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This note was uploaded on 11/01/2010 for the course ENGINEERIN PHYS222 taught by Professor Ewqfqw during the Spring '09 term at University of Washington.
 Spring '09
 EWQFQW

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