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Derivative and a function

psi20
in Analysis and Calculus

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Given the ratio of a function to its derivative, is it possible to find the function?

With just the ratio of the function to its derivative you almost have enough info to find the function. You need to solve a first order differential equation. See http://mathworld.wolfram.com/First-OrderOrdinaryDifferentialEquation.html . Your solution will have integration constants that you will not be able to determine unless you have values for the function at particular points. It may be possible to determine the function in a simpler way if the ratio of the function to its derivative is a simple function (like a constant).

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