Mr. Integral
Math notes/Differential Equations/First-Order Methods

Exact Equations and Potential Curves — Cheat sheet

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Core rule

M=Φx,N=Φy  ⟹  Φ(x,y)=C.M=\Phi_x,\quad N=\Phi_y\implies\Phi(x,y)=C.

Watch for

Multiplying by a factor that vanishes or blows up can change which points are admissible. State the working domain and check excluded points separately. A level curve may have a vertical tangent and fail to be one global graph.