Intereting Posts

Why is it considered unlikely that there could be a contradiction in ZF/ZFC?
Prove that the operator norm is a norm
How to find integral of sqrt(sinx cosx)
Frobenius Inequality Rank
Composition of a piecewise and non-piecewise function
For a compact logic, strong completeness follows from weak completeness
Why do we do mathematical induction only for positive whole numbers?
What is a real world application of polynomial factoring?
Interesting piece of math for high school students?
When do we have $\liminf_{n\to\infty}(a_n+b_n)=\liminf_{n\to\infty}(a_n)+\liminf_{n\to\infty}(b_n)$?
Prove that if $\lim _{x\to \infty } f(x)$,then $\lim_{x\to \infty} f(x)=0$
Interesting problem of finding surface area of part of a sphere.
Proving that if $T \in \mathcal{L}(V)$ is normal, then the minimal polynomial of $T$ has no repeated roots.
Monotonic Function Optimization on Convex Constraint Region
Divisibility by $9$

The following system of ODEs – is it recognized as distinct system, with meaningful background and uses?

$$\frac{dx}{dt} = – [x(t)]^2 – x(t)y(t)$$

$$\frac{dy}{dt} = – [y(t)]^2 – x(t)y(t)$$

- Which calculus text should I use for self-study?
- Reference request: $C^k(\overline\Omega)$ as restriction of $C^{k}(\mathbb{R}^d)$ functions on $\Omega$
- Good book for Riemann Surfaces
- Good Number Theory books to start with?
- What did Newton and Leibniz actually discover?
- Beginner's text for Algebraic Number Theory

This is probably not needed, but initial conditions: $x(t=0) = x_0, \space y(t=0) = y_0$

- Does Hartshorne *really* not define things like the composition or restriction of morphisms of schemes?
- “Honest” introductory real analysis book
- Is computer science a branch of mathematics?
- categorical interpretation of quantification
- Complete classification of the groups for which converse of Lagrange's Theorem holds
- References for Banach Space Theory
- Irrational numbers in reality
- Need Suggestions for beginner who is in transition period from computational calculus to rigorous proofy Analysis

It is a two-dimensional Lotka-Volterra equation. The most general LV-equation has applications in population dynamics, networks and chemical reactions.

I don’t recognise the ODE system, but you can obtain a solution analytically.

**Hint**: Let $u=1/x$ and $v=1/y$, as though each is a Bernoulli differential equation. You can then show that, if $x_0\neq0$ and $y_0\neq0$, a solution is given by

$$x(t)=\frac{x_0}{1+\left(x_0+y_0\right)t},\\

y(t)=\frac{y_0}{1+\left(x_0+y_0\right)t}.$$

I doubt that it has a name, but you might notice that trajectories are rays from the origin (apart from the fixed points along $x+y=0$).

- Show $\{u_n\}$ orthonormal, A compact implies $\|Au_n\| \to 0$
- Why is stable equivalence necessary in topological K-theory?
- consequence of mean value theorem?
- There is no “operad of fields”
- (Why) is topology nonfirstorderizable?
- If a covering map has a section, is it a $1$-fold cover?
- What does the expression “contains arithmetic” in the second Gödel incompletenetss theorem mean exactly?
- Complex root won't work
- $\varphi\colon M\to N$ continuous and open. Then $f$ continuous iff $f\circ\varphi$ continuous.
- Understanding a Proof for Why $\ell^2$ is Complete
- Approximation of Riemann integrable function with a continuous function
- Show that $\lim_{x\to \infty}\left( 1-\frac{\lambda}{x} \right)^x = e^{-\lambda}$
- What are the “building blocks” of a vector?
- How to choose a proper contour for a contour integral?
- All derivations are directional derivatives