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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This note was uploaded on 10/26/2011 for the course MATH 20D taught by Professor Fu during the Spring '09 term at Aarhus Universitet.
 Spring '09
 FU
 Equations, Power Series

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