Solution Found!
Suppose that y1, y2, . . . , yk are k nontrivial solutions
Chapter 4, Problem 42E(choose chapter or problem)
Suppose that \(y_{1}, y_{2}, \ldots, y_{k}\) are k nontrivial solutions of a homogeneous linear nth-order differential equation with constant coefficients and that k = n + 1. Is the set of solutions \(y_{1}, y_{2}, \ldots, y_{k}\) linearly dependent or linearly independent on \((-\infty, \quad)\)? Discuss.
Text Transcription:
y_{1}, y_{2}, \ldots, y_{k}
-infty, quad
Questions & Answers
QUESTION:
Suppose that \(y_{1}, y_{2}, \ldots, y_{k}\) are k nontrivial solutions of a homogeneous linear nth-order differential equation with constant coefficients and that k = n + 1. Is the set of solutions \(y_{1}, y_{2}, \ldots, y_{k}\) linearly dependent or linearly independent on \((-\infty, \quad)\)? Discuss.
Text Transcription:
y_{1}, y_{2}, \ldots, y_{k}
-infty, quad
ANSWER:Step 1 of 3
In this question we are given that y1, y2, . . . , yk are k nontrivial solutions of a homogeneous
linear nth-order differential equation with constant coefficients and that k = n + 1. We have to
discuss that the set of solutions y1, y2, . . . , yk linearly dependent or linearly independent on