Hi TheFerruccio,
Your work looks fine, I just went through the problem and obtain the same result you got. I have seen a lot of power series solutions that end up with three coefficients in their recursive relations, so it is no problem. This happens when you have second order differential...
The incongruence between your work and the solution quoted by Maple stems from the integrating factor. Please examine that again. And, note that Maple has (for some reason) chosen the constant of integration in your solution to be equal to unity.
Sure, looks Bernoulliriffic to me. Just trust yourself, go through the solution strategy for the Bernoulli equations, and you will arrive at a result. It is always good to try things out before asking questions. Maybe you can solve that with exact differentials + integrating factor as well...
Agreed. while v = y/x does work quite frequently (at least in your homework problems I imagine), you have probably learned about other trademark substitutions of different types of equations. Specifically, this is a Bernoulli type equation (and, it has its own characteristic substitution, and...
Further, if you are encountering this in a course on electrodynamics (Griffiths, or Jackson), the motivation for the definition of the dirac delta function is precisely this argument, and they both spend a few pages discussing this. If you would like further discussion on this that is more...
This is asking for symmetric equations of lines, that is to say, of the form:
\frac{x-x_0}{a} = \frac{y - y_0}{b} = \frac{z - z_0}{c}
right? Are you doing this? They tell you one of the forms:
\frac{z - z_0}{c} \rightarrow \frac{z}{10}
When you say that you find an equation of a line that...
Agreed, what you list as a question is different than what you actually profess confusion in understanding.
The question wants you to verify v(t) is a solution. Did you misunderstand, or did you really wish to discuss how to obtain that solution?
Duderstadt & Hamilton (D&H), as well as Lamarsh I believe, routinely use the approximation:
D \simeq \frac{\lambda_{tr}}{3} = \frac{1}{3\Sigma_{tr}} = \frac{1}{3(\Sigma_t - \bar{\mu}_0\Sigma_s)}
The diffusion coefficient D has units of length (cm) in those texts. It is also not uncommon to...
Health physics courses at the universities I am familiar with use:
(1) Lamarsh, Introduction to Nuclear Engineering (Ch. 9-11)
(2) Turner, Atoms, Radiation, and Radiation Protection, 2nd Edition
On second thought (this is edited), I will assume you understand how to find the spring constant k and just were confused about the limits, which I should have done in the first place since that is what you asked.
Can you clarify how you are setting up your expression for calculating the work...
This is for a numerical model, correct?
I think fluid dynamics would be a little too crude for this kind of calculation. How about looking into the Klimontovich equation (kinetic theory), and modifying it appropriately for this situation (\vec{B} \equiv 0)? You would track each charged...
No problem about being confused, I should be clearer.
I do not have your text in front of me so I cannot gauge the actual context the author is presenting without speculation, but what I was suggesting is that the text's motive was to list two candidate solutions y_1 and y_2, it then proceeds...
Just to be clear, the fact that this differential equation happened to have a one-term solution has nothing to do the fact that equation held repeated roots in the parameter r. This was a coincidence. We are not even usually so fortunate to be able to express a Frobenius solution in closed...
I am not sure I understand what you are saying with the whole n^2 = 0 business. Maybe a closer inspection of all posts on this thread would help me see. Put another way (or, perhaps the same way),
You found a value for r = 2 under the proviso that a_0 \neq 0. Your "recursive" relation...