Can g(x) be found to satisfy this differential equation?

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SUMMARY

The discussion centers on finding a function g(x) that satisfies the differential equation \(\frac{d g(t)}{dt} = \frac{1}{j(t) - g(t)}\). The equation arises from manipulating the original expression \(\frac{dt}{dg} - g(t) = j(t)\). Participants explore the necessary form of g(x) and the methods for solving such differential equations, emphasizing the importance of understanding the relationship between g(t) and j(t).

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Hello all,

While just mucking around and trying to get my head around some calculus topics we were doing in class, I came across the following problem. Is there a way to find a function g(x) such that it satisfies below?

[tex]{\operatorname{d}t\over\operatorname{d}g}-g(t)=j(t)[/tex]

I have no real experience in solving these types of equations; basically I am just curious to what style g(x) must be in order to satisfy this, and also, how to go about solving it if it's possible...

Cheers,
Adrian
 
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Maybe make it into a differential equation for g as a function of t ...
[tex] \frac{d g(t)}{dt} = \frac{1}{j(t)-g(t)}[/tex]
 

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