All Questions
Tagged with applications ordinary-differential-equations
117
questions
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294
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Question in population dynamics using exponential growth rate equation
Given population doubles in 20 minutes, what is intrinsic growth rate r?
Attempt: Given population doubles, using exponential growth rate we have $\frac{dN}{dt}=2N$ so $N(t)=N_0e^{2t}$ therefore r=2, ...
- 395
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31
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Determining correlations of derivatives of a function given only measurements of that function
Cross-posted from statistics stackexchange:
Say we have a permanent-magnet DC motor that roughly obeys the system equation $\ddot{x}(t) = \alpha \dot{x}(t) + \beta u(t) + \gamma$, where $x(t)$ is the ...
- 1,378
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How to solve simple differential equation (biology)
First of all, I am a biologist and I am not really knowledgeable in mathematics. Thus, I apologize if what I am asking is naive or not fully explained.
I am trying to solve analytically a differential ...
2
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0
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Thomas Calculus wrong question on Differential Equation?
The problem:
An antibiotic is administered intravenously into the bloodstream at a constant rate $r$. As the drug flows through the patient's system and acts on the infection that is present, it is ...
- 1,156
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Ray tracing in nonuniform media; did I write this second order differential equation as two first order differential equations correctly?
Both answers to the Physics SE question Ray tracing in a inhomogeneous media* arrive at some form of the equation below and one links to Florian Bociort's dissertation Imaging properties of gradient-...
- 1,893
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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
$$\frac{1}{\xi^2} \frac{\mathrm{d}}{\mathrm{d}\xi} \left(\xi^...
- 1,893
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397
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Modelling interest with differential equations (IVP)
Problem : you set a bank account, with initial value k, the bank will pay you continuous interest of 12% per year.
a) write an initial value problem for your account balance y(t) after t years
Sol:
$$...
- 69
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2
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878
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1st order linear differential equation application in electric circuits
I have the following 1st order linear differential equation: $$L\frac{dI}{dt}+RI=E_0\sin(wt).$$
where $L$, $R$ and $E_0$ are constants. The goal here is to discuss the case when $t$ increases ...
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1
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264
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Mathematical expression for physical forces in pendulum ODE
A 16 lb weight is suspended from a spring having a spring constant of 5 lb/ft. Assume that an external force given by
24 sin (10t) and a damping force with damping constant 4, are acting on the spring....
- 612
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1
answer
54
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Hyperbolastic rate equation of type II already has its initial condition in it?
I'm modelling some real-world gene expression data with various growth models including linear, exponential, and Verhulst growth but not all of the genes are showing these forms of time-dependence. ...
- 1,876
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427
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Finding the formula for T from Newton's Law of Cooling
I think I got a wrong answer because I skipped a particular step which seemed optional. I'm still not too sure what happened though and would appreciate your help...
Background:
Newton’s law of ...
- 13
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50
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Analytic method for ODE problem
I am studying on a drag force ODE. My question is:
Is there any analytic method to solve $$\frac{dv}{dt}+\alpha v^n=g\\ n \in(1,2]$$ It is somehow look like Bernoulli Differential Equations $y' + p\...
- 25.2k
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121
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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
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Help with understanding a differential equation model related to food supply per capita
The growth rate of a population can depend on many factors. For
example, it can depend on the amount of food per capita $A$. If $A_0$
is the mimimum amount of food required, one can think of the ...
- 1,598
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Name and application of a nonlinear ODE
Is there a name for an ODE taking form:
\begin{equation}
\left(\frac{dy}{dx}\right)^2 + a y = 0,
\end{equation}
and if there is, what is the constant `a' called either generally or in certain ...
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