Math Forum / Mathematics / Undergraduate Math / May 2005

Hi, could anyone tell me how to write a regular expression that matches all words over alphabet {a, b} and DOES NOT contain 3 consecutive a's  ??
Thanks a lot

I'm trying to solve the following differential equation:
dy/dx = (1+y^2)/(1+x^2)
I assumed that this was a seperable equation and so rearranged to get:
dy/(1+y^2) = dx/(1+x^2)

Find all solutions in integers m and n to
1997^(1001)*(m^2-1)-2*m+5=3*C(2003^2004,n)
C denotes combination.

Hey guys,
I have been told that the mean values theorem
f'(c) = (f(b) − f(a))/(b − a) for f : [a, b]  R -> Rn continuous does not hold true.  Can anybody think of a simple counterexample that would prove that it is not true?  My brain does not seem to be functioning properly :)

I would like to show that if G is a group and H_1 and H_2 are
subgroups of finite index, then the intersection of H_1 and H_2,
hence denoted by H_3, also has finite index.  Here's what I have
but I don't think it works.  Let (G:H_n) be the index of H_n in G.

Task is to solve following differential equation problem with proper
substituion which is NOT given
    y' = (x + y - 1)^2
if it's not problem please comment it...

  I have a Linear Algebra (LA) mid-term but I'm not too sure what the
best method is for preparing for it. For Calculus, I made flash-cards
which works well with formulas and derivations (e.g. "What is the
derivative of sin(x)?" on the back, cos(x)") but LA seems a whole new

Hi can anyone help me with solving the DE;
dy/dx + 25y = 10(cos5x-2sin5x)
by using Laplace transforms.
Thanks

This doesn't make sense to me
If two linear lines intersect at angle PI/2 , then the slopes k1 and k2 for those two lines are k1=-1/k2
Can someone tell me why ?
Also , since k1=-1/k2 -> tan a=| [k1-k2]/(1+k1*k2) | -> and since denominator 1+k1*k2=0 , it means :

Hello, Everyone! :)
This one should sound easy but here it goes anyway:
What's the probability that AX^2 + BX + C = 0 has real roots if A, B, C are independent random variables with Uniform (0,1) distribution?

I have a text that gives an example of using a Green's function to
determine the particular solution for a class of differential equations
(D^2 + 1).
At one point he gives this equation:

For which fields F is the additive group (F,+) cyclic?

Is there any resource on the webb where I can find formulas to the most common fractals, like the Julia?
I only need the raw formulas, like for instance the Mandelbrot formula
z= z*z+c
When I have that, I can program the rest.

How many dimensions does it have?

A Spring is suspended from a ceiling. When a mass weighing 60 lb is attached, the spring is stretched 1/2 ft. The mass is removed and a person grabs the end of the spring and proceeds to bounce up and down with a period of 1 second. How much does the person weigh?