All Questions
Tagged with applications ordinary-differential-equations
117
questions
0
votes
1
answer
44
views
The differential equation of the change of the amount of the nutrition inside of the incubator. [closed]
The problem statement is as below.
We will handle the incubator with the microbes inside of it.
The microbe increases consuming a nutrition.
The amount of the nutrition is never increased.
$10^3*P(t):=...
user802763
0
votes
1
answer
36
views
Finding out the transer function where the equation of the input function and the output function are given
$G(s):=$The transfer function which I want to find out.
$f(t):=$The input function of some system.
$x(t):=$The output function of some system.
The below equation being given.
$4\frac{dx(t)}{dt}+3x(t)=...
user802763
1
vote
0
answers
45
views
Conceptual complex dynamics - Is it reasonable to perform bifurcation diagrams on PDE's?
I am working on a PDE model, the subject has been modeled with ODE's before. The articles usually have a bifurcation diagram, and to be able to validate my model, I want to compare my work with the ...
- 53
1
vote
1
answer
210
views
Criterion to see if you can neglect air drag in projectile motion
In physics education you often consider "real world problems" with projectile motion. Most times in introductory courses you neglect air drag. But how can students (knowing nothing about ...
- 987
0
votes
0
answers
92
views
Derive the equations of motion and determine whether angular momentum is conserved..
Suppose that the gravitational force is not given by the inverse-square law, and instead is
$$ F_{grav}=\left(\frac{A}{r^{2}}+\frac{B}{r^{4}}\right)\hat{r}, $$
where A and B are real constants. Derive ...
- 1
1
vote
0
answers
46
views
Differential equation undamped system
Question image
How can I solve this question?
An object weighting 8 pounds is suspended from a spring stretching it 0.5 feet. The weight, which
is at rest in the equilibrium position, is struck an ...
- 11
0
votes
0
answers
64
views
Differential Equation Application of Physics-Sliding Block
Where I can I start to solve this question?
A block is released with an initial velocity v0 = 20 m/s from the bottom of an inclined plane
making an angle of 30◦ with the horizontal. If the constant ...
- 11
1
vote
1
answer
145
views
Basic ODE story - tank with pumps
Full tank has $500$ liter of water containing $0.2\%$ of salt. One pipe pumps clear water in ($100$ liters per minute) and the other gets the mixture from the tank ($100$ liters per minute too). ...
- 2,190
-1
votes
1
answer
103
views
Calculating if Romeo and Juliet will stay together always or not. [closed]
I have two equations which describe the Love of Romeo for Juliet (R) and Love of Juliet for Romeo (J) as a function of time, $t$.
$R=-c_1e^{3t}-c_2e^{2t}$
$J=2c_1e^{3t}+c_2e^{2t}$
They will stay ...
- 25
1
vote
1
answer
39
views
perfect lens: expression for interface
Suppose I want to find a function $(x,z) \mapsto y((x^2+z^2)^{1/2})$ which must represent the interface between two translucent media with different refractive index and which must yield a perfect ...
- 2,455
0
votes
2
answers
3k
views
Applications of the Laplace Transform
I am curious to know what kind of applications the Laplace transform has. Yes, I know people will reference Wikipedia, and other online sites which discuss the Laplace transform at length. However, ...
- 5,190
1
vote
1
answer
87
views
Approximation for Lambert W containing exponential, to help simplify ODE
I have a linear ODE derived from electrical engineering of the form:
$$\omega\cos(\omega t) - W\left(\frac{e^{\omega\cos(\omega t)}}{C}\right) = \frac{Ai'(t)}{i(t)}$$
Where A, C are constants, and W ...
- 2,323
1
vote
1
answer
46
views
Which logistic equation is better for solving this question?
So I was given a question about spread of disease:
A virus is spreading through a city of 50,000 people who take no precautions. The virus was brought to the town by 100 people and it was found ...
- 13
1
vote
1
answer
444
views
Applications of coupled systems of $\;2\times 2\;$ linear differential equations
I am providing maths help to some students studying just before University level in mathematics.
I am writing some practice questions for them on solving coupled first order linear equations and I ...
- 3,182
0
votes
1
answer
211
views
Solutions of the Falkner Skan Equation for Negative Beta
I was wondering what the solution to the Falkner Skan equation, $$f^{\prime\prime\prime}+ff^{\prime\prime}+\beta(1-f^{\prime 2})=0$$ looks like for negative values of $\beta$ and whether solutions for ...
