Intereting Posts

Prove that if f in $C(X \times Y)$ then there exists functions.
Proof of the relation $\int^1_0 \frac{\log^n x}{1-x}dx=(-1)^n~ n!~ \zeta(n+1)$
Check my answer: Prove that every open set in $\Bbb R^n$ is a countable union of open intervals.
$G$ is locally compact semitopological group. There exists a neighborhood $U$ of $1$ such that $\overline{UU}$ is compact.
book with lot of examples on abstract algebra and topology
Binomial Expansion where N is negative
Car parking related probability
closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+…+\binom{n}{n}$
n-th roots of unity form a cyclic group in a field of characteristic p if gcd(n,p) = 1
Proving $\gcd( m,n)$=1
Why is a covering space of a torus $T$ homeomorphic either to $\mathbb{R}^2$, $S^1\times\mathbb{R}$ or $T$?
Proving that cardinality of the reals = cardinality of $$
Norm is weakly lower semicontinuous
Can there be a set of numbers, which have properties like those of quaternions, but of dimension 3?
Composition of a weakly convergent sequence with a nonlinear function

I have this system of ODEs:

$$x’=-y+ \mu x(x^2+y^2)$$

$$y’=x+ \mu y(x^2+y^2)$$

- Does the Cauchy-Lipschitz theorem extend to higher order DEs?
- What is an example of a second order differential equation for which it is known that there are no smooth solutions?
- Solve a system of second order differential equations
- How can I find all solutions to differential equation?
- I need help with Differential equations.
- Determine the *interval* in which the solution is defined?

I already find that in $\mathbb{R}^2$ the only singular point is $(0,0)$. So I have to blow-up the singularity to find the phase diagram. For that I use polar coordinates, the problem is that I get a system of the form

$$r’=\mu r^3$$

$$r^2\theta’=r^2$$

so $\theta’$ is never zero, but I’m pretty sure that the system has at least 2 singular points, any ideas about how to solve this problem?

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- Differential equation for Harmonic Motion
- Finding Weak Solutions to ODEs
- Properties of sin(x) and cos(x) from definition as solution to differential equation y''=-y
- Solve a system of second order differential equations
- Looking for a Simple Argument for “Integral Curve Starting at A Singular Point is Constant”
- Particular solution to a Riccati equation $y' = 1 + 2y + xy^2$

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- Correspondence theorem for rings.
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- Prove this : $\left(a\cos\alpha\right)^n + \left(b\sin\alpha\right)^n = p^n$
- $p$ divides $n^p-n$
- Convex metric on a continuum.
- Why does $\int\limits_0^1 {\dfrac{{x – 1}}{{\ln x}}} \;\text{d}x=\ln2$?
- Shortest way of proving that the Galois conjugate of a character is still a character
- Determining the probability density function from an equation