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Differential equations in itself is a very complex topic. I read this article on a website that we can apply differential equations to optics and something like brachistochrone problem. What is this brachistochrone problem?

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Google is your friend. Also, you should read about the Eikonal Equation –  Pragabhava Nov 8 '12 at 7:10
You are aware of Maxwell's equations, by any chance? –  J. M. Nov 8 '12 at 7:14

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