We have been told that in the case of repeated, real roots, we can get a second, linearly indpendent solution by adding an extra t. (a) How do we know that e^rt and te^rt are linearly independent? (b) Show that the extra t idea actually works. That is, show that y(t) = te^rt is actually a solution of the repeated root differential equation y" − 2ry' + r^2y = 0.
We have been told that in the case of repeated, real roots, we can get a second, linearly indpendent solution by adding an extra t. (a) How do we know that e^rt and te^rt are linearly independent? (b) Show that the extra t idea actually works. That is, show that y(t) = te^rt is actually a solution of the repeated root differential equation y" − 2ry' + r^2y = 0.
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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We have been told that in the case of repeated, real roots, we can get a
second, linearly indpendent solution by adding an extra t.
(a) How do we know that e^rt and te^rt are linearly independent?
(b) Show that the extra t idea actually works. That is, show
that y(t) = te^rt is actually a solution of the repeated root differential
equation y" − 2ry' + r^2y = 0.
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