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A solution specified by a relation $F(x,y)=C$, instead of by an explicit graph $y=f(x)$. Differentiating the relation verifies its ordinary differential equation. Where $F_y\ne 0$, the implicit function theorem supplies a local graph; other points may require a different parameterization.

A level curve is the planar level set of a scalar function. Where the gradient does not vanish, the implicit function theorem makes it locally a smooth curve. At a critical point, branches may cross, narrow into a cusp or shrink to a point, so a plot should be interpreted with the local critical-point analysis.