у+ Хо 7. y" + xу' +2y = 0, xo = 0 =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
7 pl
, show that yı
and y2 form a fundamental set of solutions.
d. If possible, find the general term in each solution.
1. y" - y = 0, xo = 0
2. y" + 3y' =0,
xo = 0
bahAbne
3. y"-xy' - y = 0,
y" - xy' - y = 0,
y"+k²x²y = 0,
(1-x)y"+y=0,
y" + xy' + 2y = 0,
xy" + y + xy = 0,
4.
5.
tedious. A symb
specified number of terms in a pow
suitable graphics package we can a
section.
xo = 0
Xo = 1
xo = 0, k a constant
xo=0
xo = 0
xo = 1
y" - xy' - y = 0,
12.
13. y" + xy' + 2y = 0,
14.
17
6.
7.
8.
9.
(3-x²) y" - 3xy' - y = 0, xo = 0
10.
2y" + xy' + 3y = 0, xo=0
11. 2y" + (x + 1) y' + 3y = 0, Xo = 2
In each of Problems 12 through 14:
a. Find the first five nonzero terms in the solution of the given
initial-value problem.
G b. Plot the four-term and the five-term approximations to the
solution on the same axes.
c. From the plot in part b, estimate the interval in which the
four-term approximation is reasonably accurate.
of
of
1:
(1-x)y" + xy' - y = 0, y(0) = -3, y'(0) = 2
V
i
y(0) = 2, y'(0) = 1; see Problem 3
y(0) = 4, y'(0) = -1; see Problem 7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22b1319c-242c-4915-8f56-7c035e43f773%2F8adb562a-2cf2-4611-8f68-d97679900be1%2Fn02c47q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problems
In each of Problems 1 through 11:
a. Seek power series solutions of the given differential equation
about the given point xo; find the recurrence relation that the
coefficients must satisfy.
b. Find the first four nonzero terms in each of two solutions yı
and y2 (unless the series terminates sooner).
c. By evaluating the Wronskian W[y₁, y2](xo), show that yı
and y2 form a fundamental set of solutions.
d. If possible, find the general term in each solution.
1. y" - y = 0, xo = 0
2. y" + 3y' =0,
xo = 0
bahAbne
3. y"-xy' - y = 0,
y" - xy' - y = 0,
y"+k²x²y = 0,
(1-x)y"+y=0,
y" + xy' + 2y = 0,
xy" + y + xy = 0,
4.
5.
tedious. A symb
specified number of terms in a pow
suitable graphics package we can a
section.
xo = 0
Xo = 1
xo = 0, k a constant
xo=0
xo = 0
xo = 1
y" - xy' - y = 0,
12.
13. y" + xy' + 2y = 0,
14.
17
6.
7.
8.
9.
(3-x²) y" - 3xy' - y = 0, xo = 0
10.
2y" + xy' + 3y = 0, xo=0
11. 2y" + (x + 1) y' + 3y = 0, Xo = 2
In each of Problems 12 through 14:
a. Find the first five nonzero terms in the solution of the given
initial-value problem.
G b. Plot the four-term and the five-term approximations to the
solution on the same axes.
c. From the plot in part b, estimate the interval in which the
four-term approximation is reasonably accurate.
of
of
1:
(1-x)y" + xy' - y = 0, y(0) = -3, y'(0) = 2
V
i
y(0) = 2, y'(0) = 1; see Problem 3
y(0) = 4, y'(0) = -1; see Problem 7
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