Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
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Transcribed Image Text:20
444
Chapter 8 Series Solutions of Differentia
In Problems 19-24, find a power series expansion about
x = 0 for a general solution to the given differential equa-
tion. Your answer should include a general formula for the
coefficients.
19. y' - 2xy = 0
20. y" + y = 0
21. y" - xy' + 4y = 0
22. y" xy = 0
23. z" -x²z' - xz = 0
24. (x²+1)y" - xy' + y = 0
In Problems 25-28, find at least the first four nonzero terms in
a power series expansion about x = 0 for the solution to the
given initial value problem.
25. w" + 3xw' - w = 0;
w(0) = 2, w'(0) = 0
26. (x²-x+1)y" - y' - y = 0;
y(0) = 0, y' (0) = 1
27. (x+1)y" - y = 0;
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