UMBC Dept of Math & Stat

Errata in Farlow's Differential Equations — Chapter 1

Page 15:
(Spotted by Dr. Bradley) In the text just after equation (2), the $y^{(n)}$ should be $y^{(n-1)}$, as in: where $f$ is a function of $x, y, y', \ldots, y^{(n-1)}$.
Pages 18 and 19, Example 5:
(Spotted by Dr. Elliott Bertrand) In the statement of the problem on page 18, the equation $x^2+y^2=c$ is meant to be be $x^2+y^2=c^2$. That incorrect form of the equation appears two more times in the second paragraph on page 19. Additionally, at the end of that paragraph the expressions $y = + \sqrt{c-x^2}$ and $y = - \sqrt{c-x^2}$ should be $y = + \sqrt{c^2-x^2}$ and $y = - \sqrt{c^2-x^2}$.

Furthermore, the statement of the problem on page 18 is garbled. The line
$\quad$“where $c$ is a positive constant and is an implicit solution of $\ldots$”
should be
$\quad$“where $c$ is a positive constant, is an implicit solution of$\ldots$ ”.

Page 23, last paragraph:
(Spotted by Dr. Peercy) The expression $\partial f/\partial y = \frac13 y^{2/3}$ should be $\partial f/\partial y = \frac13 y^{-2/3}$.
Page 26, Exercise 26(b):
(Spotted by Andrew Zuelsdorf) The answer in the back of the book is $\frac{x^3}{3}$. It should be $\frac{x^3}{3}+c$.



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Author: Rouben Rostamian