Tagged Questions

DO NOT USE THIS TAG just because the question contains a differential equation!

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Contradictory argument to continous energy spectrum in quantum mechanics

The Schrodinger equation can be formulated as a regular Sturm-Liouville problem along with proper boundary conditions. Now the solution of regular Sturm Liouville problems with suitable boundary ...
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How can I get the boundary and initial conditions of the convection–diffusion equation consistant?

I want to solve the 1D convection–diffusion equation. The boundary conditions are a flux in from the bottom and a flux out on the top. Furthermore I want no concentration inside at the beginning. I ...
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Is there a proof that the number of eigenstates is countable for a bound system?

When you solve Schrödinger equation for a free particle with no boundary conditions your eigen states are indexed by quantum number $k \in \mathbb R$ and $\mathbb R$ isn't countable but if you add a ...
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Spring-mass system with variable stifness $m \ddot{x}+k(x)x=0$, time period is known, stifness is unknown

This question is somewhat related to my previous question: What is the time period of an oscillator with varying spring constant? In that question, time period of mass-spring system with variable ...
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When to use separation of variables in E&M? [closed]

I'd really like to know if there is a fast way to recognize if separation of variables is the most appropriate way to go about solving a problem. Are there any kind of guidelines for when to use ...
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Is there any physically relevant example of constructing series solution about infinity of an ordinary differential equation?

I was reading about how to test if a given second order ordinary differential equation has singularity at infinity from Arfken and Weber. I understood the steps mathematically but I could not find its ...
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What is meant by “method of approximate numerical method” or “method of digital computer” for solving the differential equation of resistive force?

I was reading "motion against resistive forces" in Newtonian Mechanics by A.P. French; here is the excerpt: [...] In general, the resistive force $\mathbf{R}$ is is a function of speed, so that ...
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Causality and natural modeling of physical systems using integral forms [closed]

I posed a closely related question here but it received a tumbleweeds award. So I thought I would post it from a different angle to see if I can illicit at least some thoughtful comments if not ...
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Do delay differential equations (DDEs) ever describe real-world phenomena? [closed]

I've recently become interested in DDEs, but I don't know much about them. A DDE has the form \begin{align*}\dot{x}(t) = f(t, x(t - \tau)) && \tau > 0\end{align*} My understanding ...
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Numerical modelling of a step function in time in a hydrodynamic system. (Runge Kutta fourth order)

So I'm trying to model a hydrodynamic system that introduces a sudden "jump" in the value of a function at a specific time. The system is solved with a Runge-Kutta fourth order method. I have a ...
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General solution to the wave equation proving dependence on $x \pm vt$

I am trying to solve for a general solution to the wave function and demonstrate any solution has the form $f(x,t) = f_L (x+vt) + f_R (x-vt)$ I have used separation of variables f(x,t)=X(x)T(t) to ...
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How to solve highly oscillating differential equation [closed]

The equation looks like: $$x''(t)+bx'(t)+c x(t)+dx^3(t)=0.$$ This is the motion of a particle in a potential $cx^2/2+dx^4/4$ with friction force $bx'$. In my case, the friction term is very small and ...
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Modifying differential equations representing a projectile system to account for an arbitrary force

The following series of differential equations represents a projectile's path when solved (g=9.81): Here is some sample output from this system (with initial values x,y=0, v=1500, theta=1.33): I ...
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Could you give boundary conditions to the gravitational potential given the density distribution?

We´re doing a project that's all about solving differential equations with separation of variables. We´re trying to find the gravitational potential given the density distribution (that has azimuthal ...
It is known that in the partial differential equation: $$u_t=au_{xx}$$ within the limits $0<x<1$ and $a>0$, the diffusion coefficient, arises in the mathematical modelling of a process of ...