All Questions
Tagged with applications ordinary-differential-equations
117
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Interpreting solutions to spring-mass ODEs.
I have the following spring-mass ODE solutions:
$$1:\;\;\;x(t)=-3\sin(2t)+4\cos(2t)+12t\sin(t)$$
$$2:\;\;\;x(t)=6e^{-t}\cos(3t)-3e^{-t}\sin(2t)+40\sin(7t)$$
How is is possible to figure if each one is ...
- 719
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What are some practical applications of successive differentiation?
Before starting to learn something, I always wonder whats its application. So would you please give some practical examples of application of Successive differentiation and concepts related to it such ...
- 185
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Provide a full phase plane analysis for the model
Provide a full phase plane analysis for the model:
$\left\{\begin{array}{l} \epsilon\dfrac{dx}{dt}=-(x^3-Tx+b)\;,\;T>0\\\dfrac{db}{dt}=x-x_0\end{array} \right.$
So I'm trying to find critical ...
- 462
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2
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Solution to ODE from Newton's Second Law
I have attempted to explore Newton's second law (F = ma) further into its many differential forms. I am not very familiar with differential equations and was searching for the steps and methods to ...
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Applications of differential equations that boil down to tridiagonal matrix when solved using implicit methods
I am looking for actual applications where differential equations are solved using implicit methods that boil down to solving a tridiagonal every time step. I found that there are heat equations and ...
- 157
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SIR model: condition on the equation $R_\infty = 1 - e^{-\lambda k R_\infty}$ to have nonzero solution
I was reading this paper (pages 3 and 4 if you need the context), while I saw this equation on $R_\infty$ (the number of people who finally recovered): $R_\infty = 1 - e^{-\lambda k R_\infty}$.
But, ...
- 1,478
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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
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2
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A problem with interpreting this text into actual mathematics
It is raining and a barrel of water has been filled to its maximum height of $90$ cm. Suddenly it stops raining, and the barrel of water is leaking water in such a manner that the level of water leaks ...
- 1,948
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103
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Applications of $n^{\text{th}}$ order ODE's.
I've always thought there aren't many applications of ODE's as opposed to PDE's due to it's simplicity in comparison, but I've only really dealt with problems up to the third order, and so I was ...
- 1,113
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Linear Differential Equation for Performance Level
I'm solving a question from my Calculus textbook that asks the following:
Let $P(t)$ be the performance level of someone learning a skill as a function of the training time $t.$ The graph of $P$ is ...
- 71
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Solving a Fredholm integral equation with a logarithmic kernel
I'm trying to solve this integral equation to find $y(x)$ but am struggling. Note, $a$ and $c$ are just two parameters.
$$\int_0^{\infty}y(t)\,\text{ln}\left|{\frac{t-x}{t+x}}\right|dt=\pi\left[\pi+2\...
user411267
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Can someone suggest a nice engineering application of a second order differential equation?
I am writing a case for one of applied mathematics course involving solving differential equations. Can someone suggest an engineering application of a practical problem that I can ask my students to ...
- 12.2k
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1
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435
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Gegenbauer functions and applications (esp. circular envelope special case)?
Playing around for a solver for orthogonal polynomials in differential equations I stumbled upon the Gegenbauer polynomials described on Wikipedia the other day.
They are the family of polynomials $y(...
- 26.1k
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Show that $y(t) = T(t − t_{0})$ also satisfies Newton’s law of cooling, $\frac{dT}{dt} = k(T_{e} − T)$, for any constant $t_{0}$.
This question if from MIT's Open Course Ware for Single Variable Calculus:
Show that $\:y(t) = T(t − t_{0})$ also satisfies Newton’s law of cooling, $\: \frac{dT}{dt} = k(T_{e} - T,)\:$for any ...
- 353
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Physical meaning of this boundary value differential equation
I am considering the following boundary value problem:
$$-\frac{\mathrm{d}}{\mathrm{d}x} \left[ a(x) \frac{\mathrm{d}}{\mathrm{d}x}(u(x)) \right] + c(x)u(x) = f(x),$$
where $x \in [0,1]$ and $u(0) = ...
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