Exact Equations | Curiwise

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Hook

A hidden function waiting to be found

Some equations, written M dx + N dy = 0, are secretly the total differential of a single function F(x,y). If so, the equation literally says dF = 0 — meaning F is constant. The entire solution is just F(x,y) = C. The only question is: how do you know when this hidden F exists, and how do you reconstruct it?

If M dx + N dy = dF, then the solution is simply F(x,y) = C.

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