Recent content by Precursor

I've followed your steps, but when I'm solving the case for n = 1, I get B_{1} = \beta_{1}r + r^{2}. Shouldn't it only be r^{2}?

Is the \delta_{n1}r^2 obtained in the solution by linearity? And why is the coefficient '3' not in front?

How do I solve the following Euler's equation: r^2 B_n'' + r B_n' - n^2 B_n = 3 \delta_{n1} r^2 Such that the solution is: B_n(r) = \beta_n r^n + \delta_{n1}r^2, \forall n \ge 1 where βn is a free coefficient, δ is the Kronecker delta function, and the solutions unbounded at r=0 are discarded.

The integral is part of a larger problem, which is to solve the wave equation in polar coordinates. The problem statement does not specify α(r). Should I just leave the integral as is?

I would like to evaluate the following integral which has a Bessel function J_{3}(\lambda_{m}r), and \alpha(r) is a function. \int^{a}_{0} \alpha(r)rJ_{3}(\lambda_{m}r)dr I'm unsure how to proceed due to the Bessel function. Am I supposed to use a recurrence relation? Which one?

Homework Statement The attempt at a solution I'm using the method of separation of variables by first defining the solution as u(x,t) =X(x)T(t) Putting this back into the PDE I get: T''X = x^{2}X''T + xX'T which is simplified to \frac{T''}{T} = \frac{x^{2}X'' + xX'}{X} = -\lambda^{2} The...

Homework Statement The Attempt at a Solution Is this correct?

Homework Statement The attempt at a solution I started by finding the expected frequencies corresponding to the intervals. I used the z-table for this. I got a chi-square value of 3.47. The answer, however, should be 1.98. Should I have used the z-table as mentioned earlier, or...

Homework Statement The attempt at a solution The correct approach is to apply the lumped capacitance method. However, in the lumped capacitance problems I've faced before, it never had a heat generation as it does in this problem. How do I go about solving this?

I chose a displacement of 5.0 mm because it will give me the smallest rate of change, whereas if I chose a number closer to 0, I would get a higher rate of change, which means higher sensitivity. Also, do I keep the value negative, or take the absolute value? I don't think negative...

So I would first have to take the derivative, and then plug in 5.0? Doing this I would get an answer of -0.514 V/mm. So will my final answer be 0.514 V/mm, if I were to take the absolute value?

Homework Statement The attempt at a solution First, we define sensitivity as the change of an instrument or transducer's output per unit change in the measured quantity. So to find the minimum sensitivity I simply plugged in the largest possible input (5.0 mm) into the equation: E =...

The way I've written the problem is exactly how it's given in the textbook (Fundamentals of Differential Equations, 7th edition, section 10.2, question 6).

Looks fine. If you simply want to check whether you're differentiating correctly, you could double check with wolfram alpha http://www.wolframalpha.com/input/?i=differentiate+y%3D%5B%283x%5E2+%2B5x+-2%29%5E%28sinx%29%5D". It actually does a lot more than that, so it's a pretty useful tool.

Homework Statement Determine all the solutions, if any, to the given boundary value problem by first finding a general solution to the differential equation: y" + y = 0 ; 0<x<2π y(0)=0 , y(2π)=1 The attempt at a solution So the general solution is given by: y = c1sin(x) +...