All Questions
Tagged with applications ordinary-differential-equations
117
questions
1
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Solving ODE system with less equations
In sensitivity analysis, there is a set of equations called sensitivity equations. They're obtained by differentiating your initial IVP with respect to the parameters. For example:
If your IVP is:
$\...
- 128k
0
votes
0
answers
58
views
How to formally justify fudge factor in this difference equation solution?
In Exercise $11$ from Section $3.3$ of Differential Equations With Boundary Value Problems by Polking, Boggess, and Arnold, we first develop the difference equation $P[n + 1] = (1 + \frac{I}{m})P[n],\ ...
- 1,922
-1
votes
3
answers
53
views
How to untangle the ODE $\frac{dx}{dt} = c + \frac{px}{l_0 + pt}$? [closed]
In working on this problem, I came up with the following differential equation:
$$
\frac{dx}{dt} = c + \frac{px}{l_0 + pt}
$$
where $x$ is the dependent variable, $t$ the independent, and all others ...
- 2,708
2
votes
1
answer
201
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Does there exist two functions $f, g\in C^1(I)$ for which $W(f, g) (x) >0$ for some $x$ and $W(f, g) (x) <0$ for some $x$?
$f, g\in C^1(I) $ where $I$ is an open interval and $f, g$ both are real valued.
Let $W(f,g)(x) =\begin{vmatrix}f(x) &g(x) \\f'(x)&g'(x)\end{vmatrix}$ denote the Wronskian of $f, g$ at $x\in I$...
- 13k
0
votes
1
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41
views
How to solve an ODE where the rate is directly proportional to two amounts?
Two chemicals in solution react together to form a compound: one unit of compound is formed from $a$ units of chemical $A$ and $b$ units of chemical $B$, with $a + b = 1$. Assume the concentration ...
- 4,392
0
votes
2
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44
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Query regarding approach to solve a given differential equation.
There's a equation
$$N(t) = N(t)\frac{P(t,z)}{B}-C\frac{d(P(t,z))}{dz}$$
$$N(t) = A\frac{dP(t,z)}{dt}$$
Constants:
B,
C=3.9878*10⁻⁷,
$A=0.11941$,
Variables:
N(t) is a function of t and is defined at a ...
- 66.8k
0
votes
0
answers
21
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Calculating Rate of Change and using differentials to project 3 years from now
Currently, BC is helping $R=5,000$ refugees. The number of refugees that BC must help is rising at a rate of $\frac{dR}{dt}=1,000$ refugees per year. Currently, the number of staff members is $N=100$ ...
- 785
0
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0
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80
views
Simulating Particle motion on a surface
I am working on a personal project to model the motion of a particle on a surface.
Using calculus, I parametrized a surface and then found the normal vector to that surface.
Using that normal vector, ...
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2
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1
answer
934
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Is state space representation useful for nonlinear control systems?
I understand that the state space representation is mathematically equivalent to the transfer function representation for linear systems, and that it allows us to solve the corresponding DE by finding ...
0
votes
1
answer
91
views
Understanding and Applying the Half Life Formula
Struggling with this question here:
"One percent of a substance disintegrates in $100$ years. What is its half
life?"
I'm not understanding how to apply the formula $T=\dfrac {\ln 2}k$ to ...
- 10.4k
1
vote
0
answers
58
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Simplest application of Picard-Lindelöf in the sciences
I am teaching single-variable real analysis and I want to give the students a concrete example of application of the Picard--Lindelöf theorem for a first-order ODE
$$
\frac{dx}{dt}=f(t,x),$$
where $t$ ...
1
vote
0
answers
41
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Sequence of Logic in Diffusion Problem DQ
Problem: If a tank is filled with 100 gallons of water and mistakenly added 300 pounds of salt. To fix the mistake the brine is drained at 3 gallons per minute and replaced with water at the same rate....
2
votes
1
answer
203
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Does there exists two differentiable functions $f, g$ on $I$ such that $W(f, g) (x) >0$ on $A$ and $W(f, g) <0$ on $I\setminus A$?
Let $I=(0, 1) $ and $A=\mathcal{C}\cap (0, 1) $ where $\mathcal{C}$ denote Cantor set.
$\color{red}{Question}$ : Does there exists two differentiable functions $f, g$ on $I$ such that $W(f, g) (x) >...
- 117k
6
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7
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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(\...
0
votes
1
answer
55
views
Using an expression and an equation to get an ODE to describe something.
I have an expression and an equation, that I need to use to show that ODE describes something.
Let me put it into context
I have an expression for the Rate at Anti-Freeze flows $\mathcal{IN}$
and $\...
- 1,143