Chloe's equation

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The title of this article is conjectural. While the information presented in this article is canonical, the article subject lacks an official name, thus the title is a conjecture.

"This [problem] has been particularly frustrating, and yet Chloe ... she solved it in a minute flat. Whatever alien influence she's under, it's studying this ship."
Nicholas Rush[src]
Chloe eqn2

Chloe's equation was the first mathematical problem that Chloe Armstrong, under the influence of the Nakai pathogen, solved for Dr. Nicholas Rush. (SGU: "Pathogen")

The problem, with its accompanying solution, is:

-\int g \sin\gamma \,dt = -\ddot{r}t \sin\gamma.


In integral calculus, it is trivial that

\int f(x) \,dt = t \cdot f(x)

\frac{d}{dt}\left[t \cdot f(x)\right] = f(x).

Dr. Rush, having completely mastered calculus, should have realized that

-\int \lambda \sin\gamma\,dt = -\lambda t \sin\gamma.

Thus, it is assumed that the solution to Chloe's equation is dependent on the fact that

\lambda := \ddot{r}.

However, during integration, constant variables should be ignored. Thus, it is assumed that the presence of t\! somehow allowed for g \mapsto  \ddot{r}.

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