All Questions
Tagged with applications ordinary-differential-equations
117
questions
0
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3
answers
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DE of an LR circuit [closed]
Suppose di/dt + 20i = 5 is a DE that models an LR circuit, with i(t) representing the current at a time t in amperes, and t representing the time in seconds. If the resistance of the circuit is 60 ...
- 15
3
votes
1
answer
868
views
Time reversal in Robertson's chemical reaction
I am studying the behavior of the Robertson chemical reaction,
$$\begin{array}{rl} \dot{x} &= -0.04 x + 10^4 y z\\ \dot{y} &= 0.04 x - 10^4 y z - 3 \times 10^7 y^2\\ \dot{z} &= 3 \times ...
- 179
6
votes
2
answers
259
views
Dynamical system defined with a non-abelian group
Soft question. I'm taking an introductory mini-course in dynamical systems, and the professor defined a continuous dynamical system in a topological space $M $ (or metric space, smooth manifold, or ...
- 78.4k
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votes
1
answer
684
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Finding the velocity, distance covered and terminal velocity of a skydiver
Here's the problem:
A skydiver and her equipment together weigh 192 pounds. Before the parachute is opened, there is an air drag force equal in magnitude to six times her velocity. Four seconds ...
0
votes
1
answer
251
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Hamiltonian System in economics
I was wondering if you know about any simple example of a Hamiltonian System that arises in economics or finances. I have been looking on the web, but I could only find one (with variables I didn't ...
- 627
1
vote
1
answer
733
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Practical applications of first order homogeneous ODE's
I look for real applications for homogeneous first order ODE's, i.e.
$$ y'(x) = f(x,y) $$ where $$ \exists n\in \mathbb{N} \quad {\rm s.t.} \quad f(\lambda x, \lambda y)= \lambda ^n f(x,y) \quad \...
- 345
1
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4
answers
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Finding an integral curve (applications of differential equations)
Find a curve whose distance of every tangent from the origin $ON$ is equal to the $x$ axis coordinate of the point of intersection between the curve and that tangent $OU$.
How to set up the graph for ...
- 3,479
1
vote
3
answers
158
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Practical system with the following ODE form
I was wondering if anyone is familiar with an example of a practical / real system with the following ODE form:
$\dot{x}_1= a_{11} x_1$
$\dot{x}_2=a_{21} x_1 + a_{22} x_2 + b u$,
where $u$ is a ...
- 307
0
votes
1
answer
77
views
Coming up with differential equation [closed]
This isn't for homework or anything - I came across a problem in which you start with one amoeba in a jar and you know that a single amoeba will spawn another one every three minutes. The original ...
- 535
10
votes
5
answers
7k
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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
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0
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Chemical Conversion question (diff. equations)
Two substances, $A$ and $B$ , are being converted into a single compound $C$. In the laboratory it has been shown that for these substances, the following law of conversion holds: the time of rate ...
- 89
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2
answers
1k
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What practical problems in the world can I apply Laplace Transforms to solve a $2^{nd}$ order ODE?
Kirchoff's Law for circuits is the most obvious answer... but other than that, I haven't been able to find any examples where Laplace Transforms can be used to solve a model of interesting real life ...
- 1,113
1
vote
1
answer
353
views
Do all differential equations have a integral form?
I have always found integration to be more intuitive than derivation. That makes me wonder why we see so many differential equations in applied mathematics...
Looking through Maxwell's equations, I ...
- 1,547
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1
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668
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How to perform non dimensionalization on a population model with predation?
So this problem is from my homework and I've been having some trouble with it. We have the following model of population growth where a and b are positive constants and r is a positive growth rate:
$...
- 21
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2
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Tacoma Narrows bridge collapse : mathematical explanation. [closed]
What is the exact mathematical reason behind the Tacoma narrow bridge collapse ?
I have googled about the collapse , but I didn't get a correct reason and a mathematical model.
- 73