Chapter 11.5, Problem 1TFR

True-False Review

For Questions (a)-(f), 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) The roots of the indicial equation for the differential equation

$x^2{y}^{″}-\left(x-x^2\right)y^{\prime }+\left(1+x^3\right)y=0$

are distinct and differ by an integer.