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Results tagged with differential-equations
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user 1849
Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.
2
votes
2
answers
295
views
Planar polynomial vector field for a harmonic pair of polynomials
Has the system of ODEs
$$\frac{dx}{dt}=P(x,y)\\
\frac{dy}{dt}=Q(x,y)
$$
been studied for the special case of the polynomials $P$ and $Q$ being a harmonic pair, i.e. the real and imaginary part …
- 7,127
5
votes
Questions about some parallel between polynomial and differential equation
To (Q1): Yes, see Differential Galois Theory. For example, the Galois group of the Airy equation over $\mathbb{C}$ is given by the Lie group $\operatorname{SL}_2(\mathbb{C})$.
To (Q2): Yes, see (Q4).
…
- 7,127