m206_reviewtest3_sp09

m206_reviewtest3_sp09 - Spring 2009 Monika Brannick...

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Unformatted text preview: Spring 2009 Monika Brannick Differential Equations - Math 206 Review Test 3 Name Directions: To receive full credit, show ALL your work! Good luck! 1. Use the power series method to solve the initial value problem (x − 1)y − xy + y = 0 subject to y (0) = −2, and y (0) = 6. 2. Determine the singular points of the given differential equation, and classify each singular point as regular or irregular. x3 (x2 − 25)(x − 2)y + 3x(x − 2)y + 7(x + 5)y = 0 . 3. For the differential equation 2x2 y − xy + (x2 + 1)y = 0, x = 0 is a regular singular point . (a) Show that the indicial roots of the singularity do not differ by an integer. (b) Use the method of Frobenius and the larger root of the indicial equation to obtain one solution about the x = 0. 4. (a) Show that L{y } = s2 Y (s) − sy (0) − y (0). (b) Use part (a) to solve the IVP y − y = e2t subject to y (0) = 0 and y (0) = 1. 1 ...
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