All Questions
16 questions
9
votes
2
answers
2k
views
The time-like geodesics (orbits) in the Schwarzschild spacetime
I am trying to plot Schwarzschild's orbit without invoking the geodesic equation.
As a reference I am using Chandrasekhar's Book (The Mathematical theory of Black Holes, Oxford University Press). In ...
- 196
8
votes
1
answer
623
views
Prove an identity in quantum harmonic oscillator
Problem:
In the context of quantum harmonic oscillator the eigenfunctions are given by:
$
u_n(x) = (N_n/\sqrt{b}) H_n(x/b) \exp\left[-x^2/(2b^2)\right]
$, where $N_n$ is the normalization factor:
$
...
- 3,074
6
votes
4
answers
433
views
A fraught with incorrect results ODE
I mean the following ODE
$$y''(x)+y'(x)=\exp (-2 x) y(x)^3.$$
Trying to solve it in version 13.1 on Windows 10 by
...
- 29.1k
6
votes
1
answer
339
views
DSolve: unable to solve the conditions
I have a second order differential equation with $2$ boundary conditions and want to use the following code to solve it:
...
- 838
5
votes
1
answer
374
views
Solving third order DE from fluid dynamics
I am trying to use DSolve to solve a differential equation from G. Batchelor: An Introduction to Fluid Dynamics, eq. 5.12.4:
[...] equation now reduces to
$$\boxed{...
- 47
4
votes
3
answers
306
views
Constant curvature surfaces. Revolution of the graphs of solutions to a nonlinear differential equation
I have the following differential equation:
$$\pi\cdot\text{y}(x)^2=\sqrt{1+\text{y}'(x)^2}\tag1$$
With the initial condition $\text{y}(0)=1$.
Now, I want to plot the solution in order to obtain the ...
- 2,021
4
votes
1
answer
353
views
Verification of a general solution to d'Alembert equation
I solved a nonlinear differential equation (d'Alembert one) by hand. Mathematica gives the same answer.
But I am not able to get Mathematica to verify the solution due to branch cuts.
Any one knows of ...
- 151k
3
votes
1
answer
140
views
I want to find differential of spherical besssel function at r=0 [closed]
I want to find an differential of a spherical Bessel function at r=0.
This is my reduced radial wave wavefunction.
u(r) = c*r*SphericalBesselJ[0, (b*r)/L]
c,b are ...
2
votes
3
answers
485
views
Optimization of ODE with respect to the initial condition
One has a (system) of ODEs with a one-parameter family of initial conditions. For example,
...
- 207
2
votes
3
answers
273
views
How to verify the ODE for Airy function with Mathematica?
I believe that the function AiryAi[x] satisfies the ODE y''[x]-x*y[x]==0
(see Encyclopedia of Mathematics and
Wiki and
Weisstein,...
- 29.1k
2
votes
2
answers
171
views
Unpacking a Mathematica expression returned by DSolve
I was trying to solve a system of differential equations in Mathematica and had troubles understanding what the solution looked like. So I wanted help to unpack it.
I had a system of two coupled ...
1
vote
3
answers
726
views
Problem solving Third order non-linear differential equation in Mathematica
I am trying to find an analytical solution of the following 3rd order non-linear differential equation in Mathematica: $a (f'(x))^2+f'''(x)=0$ with boundary conditions $f(0)=0$, $f'(0)=0$, $f(1)=1$, $...
1
vote
1
answer
62
views
Finding value of a function at limit zero
I want to evaluate the below function at limit zero. I tried with a function which has double differentiation for which it is giving me a finite value. For triple differentiation it is consistently ...
0
votes
1
answer
126
views
EllipticF reduction
Is it possible to reduce the following Z to Legendre form Elliptic integral of the First kind?
$$ \int \dfrac {\sec u\; du } {\sqrt{ (1- {(\nu \tan u)}^2 }} ..(1*)$$
With ...
- 3,234
0
votes
0
answers
71
views
Plugging the result of DSolve into the D.E does not yield zero
I am solving the following D.E
...
user49048
-1
votes
1
answer
240
views
spherical bessel function derivative
i want to evaluate differentiation of spherical Bessel function at r = 0 but i am not able to get a value for it. Any kind of help is appreciated
...