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Results tagged with differential-galois-theory
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user 25510
3
votes
Is every parametric function family, expressed as an elemetary function, a solution to an OD...
To derive a differential equation, you differentiate
$y=G(x,c)$ with respect to $x$ and then eliminate $c$. This elimination process is not always possible with elementary functions. For example $y=e^ …
- 91.8k
5
votes
Accepted
Is there a theory of "elementary closed form solution" at the operator level for differentia...
There are several theories which deal with this question.
One is the differential algebra, see, for example the little book
I. Kaplansky, Introduction to differential algebra,
Publ. de l'Institut de M …
- 91.8k
7
votes
Accepted
Analytic solutions to algebraic differential equation
Your belief is not correct, as Robert Israel pointed in his comment. Same for
differential equations: $yy'-(3/2)z^2=0$ has a solution $y(z)=z^{3/2}$ which is not
analytic at $0$. The correct theorem i …
- 91.8k