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practice test 2

# practice test 2 - y = 0 b Without explicitly solving the...

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Math 364 Ordinary Differential Equations Practice Test #2 1. Find two linearly independent solutions to the equation ¢ ¢ y + 2 x ¢ y + 4 y = 0 . Be sure to show convergence of any series and to show linear independence of solutions. 2. Find the general solution to each of the following differential equations for x > 0. a) x 2 ¢ ¢ y + 2 x ¢ y - 2 y = 0 b) x 2 ¢ ¢ y - x ¢ y + y = 0 c) x 2 ¢ ¢ y - 2 y = x 2 3. a) Show that x = 0 is a regular singular point of the equation x 2 ¢ ¢ y + (sin x ) ¢ y + (cos x
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Unformatted text preview: ) y = 0. b) Without explicitly solving the equation x 2 ¢ ¢ y + (sin x ) ¢ y + (cos x ) y = 0, describe its solutions. 4. Consider the equation ¢ ¢ y + e-x y = 0. a) Let f ( x ) be a solution of ¢ ¢ y + e-x y = 0. Show that y ( x ) = (-x ) is a solution of ¢ ¢ y + e x y = 0. b) Without explicitly solving the equation ¢ ¢ y + e-x y = 0, describe the behavior of its solutions in as much detail as you can....
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