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I'm currently in a differential equations course, and we are learning how to solve exact equations in the form of Mdx + Ndy = 0.

I immediately recognized this from my vector calculus class as it was used to find a potential function of a vector field (assuming the vector field was conservative). We integrated both M dx and N dy, combined them on a term by term basis and came up with a potential function.

In differential equations we start to do the same thing but then we set the resulting function from integration equal to N (or M, whichever one we didn't integrate).

I was just wondering if both of these processes have the same end goal and/or are interchangeable. If they aren't interchangeable why are they different? Seems like we get a function as an answer to each problem. The problems seem to slightly deviate from each other but I was wondering if this is just my professor's style. Thanks in advance,

Lee