Notes on Diffy Qs: Differential Equations for Engineers: Errata

This page lists major problems in the various editions. Simple typos, misspellings, and such are not listed here. Also not listed are things that were correct but simply deserved improvement. Of course, older editions suffer from recently discovered errata as well.

March 7th 2010 edition:

No known errata.

February 17th 2010 edition:

Exercise 2.4.5 is not possible. There is a typo in the frequencies. If you replace 0.8 with 1.1 and 0.39 with 0.8 the exercise will be possible. Also what was not noted is that you always get two possibilities for the mass in the formulas.
On page 54 about mid page, the formula for the complex roots is slightly off. If we want to take out an i, then we must negate what's under the square root sign (the discriminant). That is, the roots should be: $\frac{-b}{2a} \pm \frac{\sqrt{4ac-b^2}}{2a}$ .
On page 60, in the solution corresponding to complex roots of multiplicity k, the x^k should be x^k-1.
On page 60, the factorization and completing the square of the characteristic equation in example 2.3.5 has two typos in it, even though the roots are given correctly. The procedure should proceed as (r²-2r+2)²=0 and ((r-1)²+1)²=0.
Theorem 4.1.2 talks about p and q which do not appear in the theorem (they do appear in the more complicated version from chapter 5). Thanks to Sean Raleigh for this.
IODE Project III has changed (there was always some confusion about what was Project III) and now fits more after section 2.3, rather than before 2.6.
On page 75 on top, there is a typo in the expression for u₁', the x should be an argument to the cosine.
In example 2.6.1, when stating the parameters, it should say m=0.5 (the example is computed correctly, so no other changes needed).

February 8th 2010 edition:

Example 1.3.4 has a mistake in the integration of the left hand side. The solution should end up being $y=\frac{6}{x^2+2C}$ . Thanks to Leonardo Gomes for noticing this.
Example 2.4.1 (page 65) has a missing 2 in the derivation. Thus B is off, and so is C and gamma. Figure 2.2 is therefore also not correct. Also the discussion below the example is off by ω₀ (of course x'(0) = ω₀ B).
Example on bottom of page 72 and top of page 73 is off. The particular solution should have 1/6 not a 1/4.
The example on page 73 has a y missing in the equation, it should of course be y''-6y'+9y=e^3x.
In Example 6.1.7 (page 234), the inverse transform is off by an extra 1/2.
In Example 6.3.3 (page 243), the convolution is not computed correctly.
Figure on page 37 (bottom of page) has y=5 and y=0, when it should be x=5 and x=0. Thanks to Jeff Winegar for pointing it out.
Exercise 2.3.4 is hard to read as "equation" refers to the ODE (it is correct, but can be hard to understand).

January 10th 2010 edition:

Mildly ordered by severity:

Example on page 34 uses the wrong integrating factor. It is off by a constant. The correct integrating factor would be x^-4e^-4x+4. Thanks to Sean Raleigh for pointing this out.
Example 1.1.3 on page 15 has the wrong constant in front when we solve for |y|. It should be $\frac{1}{|k|} e^{-C'k}$ . It doesn't (of course) change the final solution as C' was arbitrary.
Example 1.3.3 had a minus sign error in the derivation, though it does not affect the final answer (and is not technically wrong if we allow complex logarithms...). Also first we implicitly give time in seconds and then we use minutes (again computations were OK).
Example 1.4.1 was missing a minus sign in the solution. It the solution should be y=e^x-x²-2e^-x². Thanks to Ian Simon for pointing it out.
Example on page 103 has the signs wrong. The expression for x₁ in the middle of the page should have e^tcos(t) -i e^tsin(t). The rest of the example also needs to have the signs fixed. Thanks to Sean Raleigh for noticing.
Exercise 1.1.7 has a typo making the solution very hard (without a computer algebra system). The right hand side should be a $\frac{1}{y+1}$ not $\frac{1}{y^2+1}$ .
Exercise 1.3.7 was impossible to solve as stated. Ignore this exercise (due to a copy/paste error, the equation happens to be the same as in 1.3.6, but with an impossible initial condition). It will be replaced with a different exercise in the next version of the notes.
There was a forgotten initial condition in Exercise 0.2.9 (x'(0)=0). The exercise is possible as is, but it was not what was intended.
In exercise 1.4.9, in part b, the target concetration should be 0.001, not 0.01 (obviously it can't be 0.01)
Exercise 1.5.6 is way too difficult, ignore. It will be replaced.
Exercise 1.5.1 was actually worked out as an example. It will be replaced.
Caption on Figure 1 gives the wrong equation.
Captions on Figures 1.7-1.10 have an extraneous negative sign, replace -0.1 by 0.1. The vertical scale on 1.6-1.10 is improperly rounded.

November 25th 2009 edition:

Examples on the first page of section 2.1 are wrong. The k in the equations should be k². Thanks to Thomas Wicklund for noticing.

October 23rd 2009 edition:

Exercise 2.1.8 has a missing minus sign. It should look like:
Exercise 2.1.8: Suppose $y_1$ is a solution to $y''+p(x)y'+q(x)y=0$ . Show that
$y_2(x)=y_1(x)\int \frac{e^{-\int p(x)dx}}{(y_1(x))^2} dx$
is also a solution.

September 29th 2009 edition:

Exercise 4.6.4 on page 188 is not correct. At least not what was intended. The side condition should be u(x,0) = 3 cos x + cos 3x.

May 12th 2009 edition:

Example 1.4.2 is wrong. There was an error with integration and there is a factor of 2 missing in the 5th line of the computation on page 30. Here is an updated page 29 and 30. Thanks to Thomas Wicklund for spotting this error.