Suppose that yi (x) =x² denotes a nontrivial solution of a homogeneous linear second-order differential equation (a) y +2ry - 6y = 0, and yı is defined on an interval 1. From a reduction of order method, we know that the second solution is - S P(x)dx -dx. [yi (x)]² e y2 = yı (x) / Use the given formula to find y2.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that yi (x) =x² denotes a nontrivial solution of a homogeneous linear
second-order differential equation
(a)
xy" +2ry – 6y = 0,
and yı is defined on an interval 1. From a reduction of order method, we know
that the second solution is
- SP(x)dx
-dx.
[yi (x)]²
e
y2 = yı (x) /
Use the given formula to find y2.
Transcribed Image Text:Suppose that yi (x) =x² denotes a nontrivial solution of a homogeneous linear second-order differential equation (a) xy" +2ry – 6y = 0, and yı is defined on an interval 1. From a reduction of order method, we know that the second solution is - SP(x)dx -dx. [yi (x)]² e y2 = yı (x) / Use the given formula to find y2.
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