Recent content by wadawalnut

Homework Statement I have this problem in an online assignment. Someone told me the answer, so I already got it right, but I don't know why my logic leads me to the wrong answer. The problem: The temperature u of a star of conductivity 1 is defined by u = \frac{1}{sqrt(x^2+y^2+z^2)}. If the...

Ahhhh that's why... Forgot about those sneaky absolute values. So I would have to split it up into an integral from 0 to pi/2 and a negative one from pi/2 to pi, right? That explains why the book was so quick to use symmetry, otherwise the symmetry wouldn't have been all that helpful. Thanks a...

Here's how I like to think of it. If the amount of integrals that you're doing is the same as the exponent on your units would be, then the integrand is 1. For example, if you're calculating an area, your units would be square units (exponent 2), so with a double integral the integrand is one...

Homework Statement Find the volume of the solid lying inside both the sphere x^2 + y^2 + z^2 = 4a^2 and the cylinder x^2 + y^2 = 2ay above the xy plane. Homework Equations Polar coordinates: r^2 = x^2 + y^2 x = r\cos(\theta) y = r\sin(\theta) The Attempt at a Solution So I tried this...

Thank you very much, this has been very helpful. However, how am I supposed to find the form of the linearly independent solutions near every regular singular point if there are infinitely many of them? I guess there must be a pattern. Trying that now.

Thanks for the reply, although I'm not sure I understand your procedure. Firstly, for the Frobenius method, aren't you supposed to normalize the y'' term and multiply everything by x^2 ? I guess that's not really that important, but can you explain how you found the indicial equation or how you...

Homework Statement Given the differential equation (\sin x)y'' + xy' + (x - \frac{1}{2})y = 0 a) Determine all the regular singular points of the equation b) Determine the indicial equation corresponding to each regular point c) Determine the form of the two linearly independent solutions...

How does dividing by \sin(x) help? That would leave me with \dfrac{y(x)}{\sin(x)} = A + Bx . How does this help me solve the equation? Thanks for the responses.

Thank you very much for the reply. I was actually just coming to the conclusion that there would have to be variable coefficients. However I'm still stuck knowing that y(x) = (A + Bx)sin(x) . I don't understand how it is particularly helpful to know that the second derivative of A + Bx is 0...

Thanks for the response. I believe y'' + y = 2cos(x) has the solution y = sin(x) + xsin(x) but would {sin(x),xsin(x)} be a fundamental set of solutions in that case?

I did not make a typo, that was the actual question.

Homework Statement I think there may be something wrong with a problem I'm doing for homework. The problem is: Solve the IVP with the differential operator method: [D^2 + 5D + 6D], y(0) = 2, y'(0) = \beta > 0 a) Determine the coordinates (t_m,y_m) of the maximum point of the solution as a...

Homework Statement I've been stuck on this problem for three days now, and I have no clue how to solve it. Construct a linear differential equation of order 2, for which { y_1(x) = sin(x), y_2(x) = xsin(x)} is a set of fundamental solutions on I = (0,\pi) . Homework Equations Wronskian for...

Homework Statement I got questions a) and b), but I'm stuck at c) and d). Homework Equations Kirchhoff's Loop and Junction rules. Equivalent resistance in series: Req = R1 + R2 Equivalent resistance in parallel: Req = ((R1)-1 + (R2)-1)-1 The Attempt at a Solution I really haven't gotten...