Recent content by depizixuri

No. It doesn't works. If I choose r=1, then A(x)=constant (which is correct), but R(x) is variable using this method.

It helps. It says that for dimension ##r=-1: c_1=36\pi## and helps me think out the box of treating b as a variable. Actually, those values for a and b have 10 different solutions for y(x). I'm not sure about what to make of it. Maybe one of those solutions is x². Thanks you.

Why you asked? Does the answer makes a difference? Does it help to classify the problem or know what area should it be related? Can you tell me at least what information does that gives or could give to you? I ask because it may help me to investigate it.

Do anybody knows any more specialized forum where I can ask about this?

Ok. I was reading about Hausdorff dimension, and I wanted to find a continuous, compact surface, without holes, with dimension 1 \leq r \leq 2. So, the area function A(x), to have a Hausdorff dimension r, must satisfy this equation: \epsilon A_{(\frac{x}{\epsilon})} = \epsilon^r A_{(x)}...

Sorry, you are right. Is not trivial. I was wrong. Is better to use Laplace transform, and even then you get a nasty work. Your solution is $$ f(x) = \left ( c_1 \Gamma_{\left(\frac{B}{A g i}+1\right)} J_{\left({\frac{B}{A g i}} , \frac{2 \sqrt{A C e^{g i x}}}{A g i}\right)}+c_2...

An easy way to calculate numerically is \frac{\Delta\rho}{ \Delta t } = - \frac{\Delta v_{max}(\rho - \frac{\rho^2}{\rho_{max}})}{\Delta x} So, if you know all the values at a time t, and because \Delta\rho = \rho_{t+1} - \rho_{t}, then you can calculate \rho_{t+1} this way: \rho_{t+1} =...

The exponential is easy to deal because exponents are added on multiplication.

There are many ways to solve it without previous knowledge of the solution. One is to make a Laplace or Fourier transform. It turns the problem into a very simple equation without any derivatives. You solve it, and reverse the transform.

It is a trivial solution taught at any basic course of differential equations. If you have a differential equation written as \sum_{n=0} ^m c_n \frac{\mathrm{d} ^n f_{(x)}}{\mathrm{d} x^n}=0, then is is known that the solution is an exponential function.

The solution is f_{(x)}=e^{a+bx}. You need to find the complex constants a and b.

Is not home assignment. Is personal curiosity. I want it to find the radius of a surface of revolution from which I only know the area. After some manipulation, I reduced the equation to this form. ¿Do you want to know how I got it? Meanwhile I have been told to look on the Weierstrass...

I tried to solve this differential equation: 2y+(y')^2+ax^b=0 ...but don't know what to do with it. Don't know what variable substitution to use. Tried Taylor series, but I get horrible nonlinear equations for the coefficients. Tried Mathematica, but it doesn't answer anything: In[20]:=...

I'm an aspie, and I had been asked to introduce myself after registering. That's awkward and unnecessary to me. I don't know what's the point. I'm looking for help with math.