All Questions
Tagged with applications ordinary-differential-equations
117
questions
10
votes
5
answers
7k
views
Are there examples of third-(or higher)-order linear differential equations in physics or applied mathematics?
The classical second-order linear ordinary differential equation is that named after Sturm and Liouville: formally,
\begin{equation}
(pu')'=ru.
\end{equation}
It arises naturally in many physical ...
- 1,442
10
votes
2
answers
666
views
Physical meaning of linear ODE $xy''+2y' + \lambda^2 x y = 0$
As reported by Wikipedia - Sinc function, $y(x)=\lambda \operatorname{sinc}(\lambda x)$ is a solution of the linear ordinary differential equation
$$x \frac{d^2 y}{d x^2} + 2 \frac{d y}{d x} + \lambda^...
- 7,880
10
votes
4
answers
2k
views
What is the physical meaning of fractional calculus?
What is the physical meaning of the fractional integral and fractional derivative?
And many researchers deal with the fractional boundary value problems, and what is the physical background?
What ...
- 111
8
votes
2
answers
2k
views
Differential vs difference equations in mathematical modeling
I'm reading a little about mathematical modeling and I've seen some population models based on differential equations. I've also seen some (not many) that can support both difference and differential ...
- 1,773
6
votes
2
answers
259
views
Dynamical system defined with a non-abelian group
Soft question. I'm taking an introductory mini-course in dynamical systems, and the professor defined a continuous dynamical system in a topological space $M $ (or metric space, smooth manifold, or ...
- 78.4k
6
votes
1
answer
2k
views
Background for studying and understanding Stochastic differential equations
Assume I have back ground of the following knowledge based on the textbook as :
ODE : ODE by Tenenbaum
Baby probability : Ross 's baby probability
Baby real anlysis : Bartle's introduction to real ...
- 1,975
6
votes
7
answers
10k
views
How to prove $A\cos(\omega t-\phi)$ = $a\cos(\omega t)$ + $b\sin(\omega t)$ using $e^{i\theta}$?
I want to show that $A\cos\left(\omega t-\phi\right)$ = $a\cos\left(\omega t\right)$ + $b\sin\left(\omega t\right)$
First I verified for myself through the angle addition proof that:
$$ \cos\left(\...
- 363
5
votes
1
answer
686
views
Solving Kepler's second law
Kepler's second law, about equal areas in equal times, is a differential equation: it gives velocity as a function of location.
Where are the best expository accounts of the process of solving this ...
4
votes
5
answers
757
views
Why - not how - do you solve Differential Equations? [closed]
I know HOW to mechanically solve basic diff. equations. To recap, you start out with the derivative $\frac{dy}{dx}=...$ and you aim to find out y=... To do this, you separate the variables, and ...
- 4,769
4
votes
3
answers
3k
views
Modelling with exact differential equations?
I'm teaching some very elementary differential equations to engineering students, and their constant question to me is "What's the use of this?" or alternatively "Where would we use this?" Now, I'm ...
- 840
4
votes
1
answer
253
views
What mathematics topics pertain more towards applied mathematics?
I'm entering my second year of undergrad (majoring in mathematics), and I've found that I am really bad at Linear Algebra, but very good at Calculus and Differential Equations. I'm hoping to venture ...
- 141
4
votes
1
answer
1k
views
Applications of First Order Differential Equations
Can I get help for this question please?
Suppose that a tank containing a liquid is vented to the air at the top and has an outlet at the bottom through which the liquid can drain. It follows from ...
- 95
4
votes
0
answers
121
views
Do repeated roots (and Real Jordan form) for ODE's come up in real world applications of ODE's
An equation like $y^{\prime \prime} + 2 y^{\prime} + y = 0$ has repeated roots: The characteristic polynomial is $r^2 + 2r + 1$ which has repeated roots $(-1,-1)$. Two basic solutions of the ODE are ...
- 705
3
votes
1
answer
868
views
Time reversal in Robertson's chemical reaction
I am studying the behavior of the Robertson chemical reaction,
$$\begin{array}{rl} \dot{x} &= -0.04 x + 10^4 y z\\ \dot{y} &= 0.04 x - 10^4 y z - 3 \times 10^7 y^2\\ \dot{z} &= 3 \times ...
- 179
3
votes
1
answer
219
views
Could there be exact solutions to the Lane-Emden equation for real n≥0 other than 0, 1, or 5?
This Astronomy SE answer says
With a constant $k$ and the polytrop index $n$. This is a result of the solutions of the Lane-Emden equation
$$\frac{1}{\xi^2} \frac{\mathrm{d}}{\mathrm{d}\xi} \left(\xi^...
- 1,893