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.

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.CR: Chapter 11 Review

Problem 1CR

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