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Unformatted text preview: Differential Equations test one solutions Tuesday, April 25, 2006 1 . Given the function y = 4+ Z x 2 sin s 2 ds ( a ) Calculate y (2) = 4+ Z 2 2 sin s 2 ds = 4+0 = 4 ( b ) Calculate dy dx = sin x 2 2 . Is the function y = x + 1 x a solution of dy dx + y 2 = 3+ x 2 ? Yes because: dy dx + y 2 = d dx x + 1 x + x + 1 x 2 = 1 1 x 2 + x 2 + 2 + 1 x 2 = 3 + x 2 3 . Determine whether each of the following equations is linear or nonlinear. ( a ) dy dt = t y 2 nonlinear ( b ) t dy dt = e t y cos t 2 linear ( c ) y dy dt = 4 t y nonlinear 4 . Which of the following equations is exact? ( a ) 3 x 2 4 y dx +(2 y 4 x ) dy = 0 3 x 2 4 y y ? =(2 y 4 x ) x 4 = 4 exact ( b ) dy dx + x 2 y = x or ( x 2 y x ) dx +(1) dy = 0 x 2 y x y ? =(1) x x 2 6 = 0 not exact page two 5 . Given the initial value problem t dy dt + 3 t 2 y = 4 t + 1 and y (3) = 5 determine the largest tinterval over which a unique solution is guaranteed to exist. Rewrite the differential equation as dy dt + 3 t ( t 2) 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
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