This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Mathematics 238 test three due Friday, May 27, 2005 1. Given the diﬀerential equation (x2 + 4)y + 3xy + 4y = 0 • list the singular points of the equation. • for which xvalues will a power series solution of the form
∞ ak (x−3)k converge?
k=0 2. For which values of x does the each of following power series converge? (a)
∞ (x − 4)2k k 9k k=1 ∞ (b)
k=1 a2k x2k where a2 = 1 & ka2k+2 = 3(k + 1)a2k for k ≥ 1 3. Find a power series solution about x = 0 (through the degree four term) to the ﬁrstorder initial value problem dy = x2 + y 2 dx extra credit parts of problem (3) • compare your solution to a numerically obtained solution from a math software package or website. (plot the two solutions together and compare) • compare your solution to the ﬁrst few Picard iterates. 4. Given the secondorder diﬀerential equation y + xy + y = 0 • for which values of x will power series solutions of this diﬀerential equation converge? • ﬁnd the recursion relation for the power series solution about x = 0. • write the general solution through the degree ﬁve terms. • ﬁnd the solution (through degree ﬁve terms) to the initial value problem y (0) = 0 and y (0) = 1. • estimate the accuracy of your solution of the previous part when −0.5 ≤ x ≤ 0.5. and y (0) = 1 Mathematics 238 test three, part two due Monday, June 6, 2005 5. Use the elimination method to solve the system of equations d2 x1 dt2 d2 x2 dt2 = x2 − x1 − 1 = −(x2 − x1 − 1) + (x3 − x2 − 1) d2 x
3 dt2 = −(x3 − x2 − 1) Begin the process by rewriting the system in the format (D2 + 1)x1 − x2 = −1 −x1 + (D2 + 2)x2 − x3 = 0 −x2 + (D2 + 1)x3 = 1 ...
View
Full
Document
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

Click to edit the document details