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1. 3 Problems involving superposition

Isn't the \lambda for the third harmonic \frac{2L}{3}? If you use hookes law, don't we need to know the spring constant k before using this information to solve this problem?
2. Maxwell's Speed Distribution

Sorry to keep badgering you here, but I do not see how you get \frac{1}{2}C^{-3/2}\int_{0}^{\infty}\sqrt{x} e^{-x}dx The \sqrt{x} should be an x/C no? We let x = Cv², so that makes v² = x/C. The term you are substituting for there is v² not v. That would make the integral...
3. Maxwell's Speed Distribution

Oh ok, so you are saying that the original equation should be: \int 4\pi\ (\frac{M}{2\pi RT})^{3/2} \cdot v^2 \cdot e^{\frac{-Mv^2}{2RT}} dv = 1 instead of: \int 4\pi\ (\frac{M}{2\pi RT})^{3/2} \cdot v^2 \cdot e^{\frac{-Mv^2}{nRT}} dv = 1 ?
4. Maxwell's Speed Distribution

Thanks for the reply, but I still seem to be a little lost. If I let C = \frac{M}{2RT} , that leaves me with 4 \pi \cdot ( \frac{C}{ \pi})^{3/2} \int \frac{x}{C} ... . I don't see how making the C = \frac{M}{2RT} helps me in the latter half of the integral because I have a n term in there...
5. Maxwell's Speed Distribution

Homework Statement Given Maxwell's probability distribution function, P(v) = 4\pi\ (\frac{M}{2\pi RT})^{3/2} \cdot v^2 \cdot e^{\frac{-Mv^2}{nRT}} Where v = velocity, M = molar mass, R = Universal Gas Constant, n = # of mols, T = temperature, solve \int P(v) dv =1 from 0 to...
6. Experimental Proof of Electrical Charge

Hi, I have a question about the transfer of electrical charge from object to another. Basically, my professor stated that if you rub a rod with certain matierials, the rod will become charged. This is due to the convention that Ben Franklin came up with called the triboelectric series. So...
7. Find the Potential as a function of position

Homework Statement A rod of length L carries a charge Q uniformly distributed along its length. The rod lies along the y-axis with one end at the origin. Find the potential as a function of position along the x-axis Homework Equations dV=\vec{E}\cdotp d\vec{l} V=\frac{kq}{r}...
8. Explaination of Curvature

Awesome, thanks guys. You really cleared this up for me!
9. Explaination of Curvature

Homework Statement Find the curvature of y = x³ Homework Equations k(x) = \frac{f"(x)}{[1+(f'(x))²]^{3/2} The Attempt at a Solution k(x) = \frac{6x}{(1+9x^4)^{3/2} I got the answer numerically, but I am looking for an explaination of the graph itself. I chose a relatively...
10. General initial value problem (DE's)

Homework Statement a) Consider the initial value problem \frac{dA}{dt} = kA, A(0) = A_0 as the model for the decay of a radioactive substance. Show that in general the half-life T of the substance is T = -\frac{ln2}{k} b) Show that the solution of the initial-value problem in part a) can...
11. Help with a simple Diff Eqn

Oh cool, even better. Thanks!
12. Ok, so now how do you separate this one?

Yes you did AKG, sorry about that. I just did not see how to factor them. I guess I am not very strong with my factoring and it was not very clear to me. Thanks for the hint Daniel, that will help me out a lot. Ok, going to go and work this out now!
13. DE with an initial condition

I am asked to solve this DE with the initial condition of y(1) = 1. (x+y)^2dx + (2xy + x^2-1)dy = 0 So, after working the problem out, I came to this as an answer: F(x,y)=\frac{1}{3}x^3 + x^2y + xy^2-y My question is what do I do with the initial condition. I assume that I am just...
14. Explanation of this Partial?

\frac{\partial_P}{\partial_y}(2ysinxcosx-y+2y^2e^{(xy^2)} I worked the first part no problem, but the second part I needed a little help from my calculator. This is what I got: 2sinxcosx-1+4ye^{(xy^2)} My question is, why does the partial of 2y^2e^{(xy^2)} come out to 4ye^{(xy^2)}...
15. Ok, so now how do you separate this one?

ok, so I tried it and I got 1+\frac{5(x-y+1)}{xy-2x+4y-8} which does not seem to help me out too much. The form of both the numerator and the denominator do look a little suspicious. Is there a way to factor them like we can for a problem in the form ax^2 + bx + c?
16. Ok, so now how do you separate this one?

Could you please be a little more specific? Do you mean just divide the two using long division? Hmmm... ok, I will try that and see if I can get to something. Thanks.
17. Did I solve this DE correctly?

Also, one quick question. Does the equation have to be in the form of P(x.y)dx + Q(x,y)dy = 0? Can it be minus instead of plus? The reason I ask is because I vaugly remember hearing something about that at the begining of the school quarter and can't seem to find it in my notes now. Thanks!
18. Did I solve this DE correctly?

If someone has a chance out there, could you please check my math here and let me know if I am doing this correctly or not. Problem: Solve: (2x-1)dx + (3y+7)dy = 0 I would like to solve this using the "Exact" method for solving DE's, so: \frac{\partial_P}{\partial_y}(2x-1) = 0...
19. Ok, so now how do you separate this one?

umm... Sorry if this sounds lame, but I don't see what I am to factor here.
20. Ok, so now how do you separate this one?

\frac{dy}{dx}=\frac{xy+3x-y-3}{xy-2x+4y-8} I want to solve this DE using the separation technique. Any ideas on how to start? And just for myself, and maybe anyone else. Is there a sort of systematic approach to finding out how to start these problems? It seems like I will work a few no...
21. Idea of how to separate?

Oh man, haha.. I like the substitution method, but I am not too keen on the trig substitution. Although, this one seems pretty nice for that. Do you mind taking a look at my partial fraction work? I need some practice with it so I was wondering if I did it correctly...
22. Idea of how to separate?

Thanks, I will try that out. To get the LHS w/o partial fractions: \int{\frac{ydy}{(y+1)^2}} let u = y+1, du = dy, and y = u-1 So, \int{\frac{(u-1)}{(u)^2}du} = \int{\frac{u}{u^2}-\frac{1}{u^2}du} = ln|u| + \frac{1}{u} Substitute y+1 for u and get ln|y+1|+\frac{1}{y+1}
23. Idea of how to separate?

Yes I have worked with partial fractions a little bit, but I don't see how it applies to this one. I don't mean to second guess you, but are you sure the LHS is not correct? I worked it out again and got the same answer and my TI-89 gives the same answer as well.
24. Idea of how to separate?

Cool Thanks. So I worked this one out and got the left hand side of the equation, but I can seem to get the integration on the right. \frac{ydy}{(y+1)^2} => \frac{dx}{(1-x^2)} = \int{\frac{ydy}{(y+1)^2}} = \int{\frac{dx}{(1-x^2)}} so, ln|y+1|+\frac{1}{y+1} = \int{\frac{dx}{(1-x^2)}}...
25. Idea of how to separate?

Ok, so I worked it out some more and got \frac{ydy}{(y+1)^2} = \frac{dx}{(1-x^2)} Is this correct?
26. Idea of how to separate?

Problem: (y-yx^2)\frac{dy}{dx} = (y+1)^2 So, the first thing I tried was just dividing the whole equation by (y-yx^2) and then factored out the y to get \frac{dy}{dx} = \frac{(y+1)^2}{y(1-x^2)}. Next I expanded the numerator on the right side of the equation and then split them all into...
27. Integral and series

Oh I see, well, just in case you want to know, the binomial expansion series says you can expand a binomial according to the following formula: 1+kx+\frac{k(k-1)}{2!}x^2+\frac{k(k-1)(k-2)}{3!}x^3 and so on, where k is your exponent. In this integral, \int{\sqrt{x^3 +1}} your function is...
28. Help with a simple Diff Eqn

Awesome, that was super easy once you look at it that way. Thanks, now I can look at other integrals and apply the same method. Life somehow just became much easier!! ^_^ Thank you!!!
29. Help with a simple Diff Eqn

I came accross another integral that I am not catching here that seems to be along the same line as this one. Is there a rule to dealing with these kinds of integrals? \int{\frac{x^2}{(1+x)}}dx
30. Help with a simple Diff Eqn

Here is the problem: Solve, (x+1)\frac{dy}{dx} = x + 6 Here is what I tried: I moved all the x's to one side and left the dy on the left of the equal sign to solve with the separation of variable method. I got, \int{dy} = \int{\frac{(x+6)}{(x+1)}dx} So here I just solve the...