Chapter 1.3, Problem 1TFR

True-False Review

For items (a)–(g), 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 from the text. If false, provide an example, illustration, or brief explanation of why the statement is false.

If $f\left(x,y\right)$ satisfies the hypotheses of the Existence and Uniqueness Theorem in a region R of the $xy$-plane, then the solution curves to a differential equation $\frac{dy}{dx}\text{= }f\left(x,y\right)$ cannot intersect in R.