Questions tagged [differential-algebra]

Differential algebra is the study of differential rings and fields and related structures.

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The antiderivative of $e^{x^2}$

I am asked to show that show that the antiderivative of $e^{x^2}$ cannot be expressed as $R(e^x)$, where $R$ is a rational function over the reals. Can this be shown without using transcendental ...
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What non-algebraic methods do we have to solve this equation?

I'm recently studying homogeneous linear second order ODEs, and got into the integrating factors technique. For every equation, if the integrating factor is known, we can reduce its order provided ...
1 vote
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Magma - Differential field extension over a differential field

I want to construct the differential field $\mathbb{Q}(x,\,\log x,\,\log(\log x))$ in Magma. I have tried the following: ...
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Can the formation of Kähler differentials be seen as a functor into the category of modules (without specifying the ring of scalars)?

In an Algebraic Geometry course, I've seen the definition of the $A$-module of Kähler differentials $\Omega_A^1$ given a $k$-algebra $A$ ($k$ is a field). Then if $X$ is a variety, we defined the ...
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q-Leibniz Rule?

The famous Leibniz rule: $(uv)' = u'v+uv'$ can be generalized for any order derivative using the following formula $$(uv)^{(n)} = \sum_{k=0}^n{n\choose k}u^{(n-k)}v^{(k)}$$ This is a known formula ...
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Find the equation of the orbit of following ODE

We call orbit associated to the initial datum $(t_0,x_0)$, the set of points: $C=\{$x$(t;t_0,x_0), t \in T\}$. Given the Matrix A: \begin{pmatrix}  0 & 1 \\ -1 & 0 \end{pmatrix} Write the ...
• 424
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Differential algebra in Wikipedia and nlab

The difference between the two definitions is clear in Wikipedia and nlab regarding the definition of a graduated algebra. How to explain this nuance? From Wikipedia: A differential ring is a ...
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1 vote
Definition of $\mathfrak{g}$-differential graded algebra
I am reading Group actions on manifolds by Eckhard Meinrenken (Lecture Notes, University of Toronto, Spring 2003). In page $45$, definition $5.2$, author introduce the notion of $\mathfrak{g}$-...