Chapter 8.1, Problem 1TFR

True-False Review

For Questions (a)-(j), decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem in fact from the text. If false, provide an example, illustration, or brief explanation of why the statement is false.

A regular $n\text{th}$-order linear homogenous differential equation defined on an interval $I$ always has $n$ solutions that are linearly independent on the interval $I$.