Errata in Farlow's Differential Equations — Appendix and Back Cover

Page 569:

(Spotted by Menachem Greenfeld) In the next to last step in equation (5), the denominator is $c^2 - cdi + cdi - d^2i$ but it should be $c^2 - cdi + cdi - d^2i^2$.

(Spotted by Kevin Stern) In that same fraction, the $+bdi^2$ in the numerator should be $-bdi^2$. As a result, the $ac-bd$ in the final result of equation (5) should be $ac+bd$. In summary, equation (5)'s final form is \[ =\Big( \frac{ac+bd}{c^2+d^2}\Big) +\Big( \frac{bc-ad}{c^2+d^2}\Big)\,i \]

Page 571:

(Spotted by Kevin Stern) Near the bottom of the page, the expression $F'''(x) = 6\sin2x -6i\cos2x$ should be $F'''(x) = 8\sin2x -8i\cos2x$.

Page 573, Exercise 3:

(Spotted by Paul Rydeen) The denominator in the expression for $z$ should be $2$ rather than $\sqrt{2}$.

Inside back cover:

(Spotted by Menachem Greenfeld) There is an extraneous parenthesis in formula 17. The correct expression is: \[ \int \sqrt{u^2 \pm a^2} \, du = \frac{1}{2} \Big( u \sqrt{u^2 \pm a^2} \pm a^2 \ln \big( u + \sqrt{u^2 \pm a^2} \, \big) \Big) \]