Suppose that yı (x) =x² denotes a nontrivial solution of a homogeneous linear second-order differential equation (а) Py +2ry - 6y = 0, and y, is defined on an interval I. From a reduction of order method, we know that the second solution is e-S P(x)dx -dx. y2 = yı (x) / [yi (x)]² 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
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Suppose that yı (x) =x denotes a nontrivial solution of a homogeneous linear
second-order differential equation
(a)
Py+2ry -6y = 0,
is defined on an interval I. From a reduction of order method, we know
and
that the second solution is
y2 = yı (x) /
e-SP(x)dx
-dxp.
bi (4) dx.
Use the given formula to find y2.
(b)
Solve
y-4y = ( - 3) sin 2r,
by the method of undetermined coefficients.
Transcribed Image Text:Suppose that yı (x) =x denotes a nontrivial solution of a homogeneous linear second-order differential equation (a) Py+2ry -6y = 0, is defined on an interval I. From a reduction of order method, we know and that the second solution is y2 = yı (x) / e-SP(x)dx -dxp. bi (4) dx. Use the given formula to find y2. (b) Solve y-4y = ( - 3) sin 2r, by the method of undetermined coefficients.
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