equality (definitional?, propositional, computational, judgemental, extensional, intensional, decidable)
isomorphism, weak equivalence, homotopy equivalence, weak homotopy equivalence, equivalence in an (∞,1)-category
Examples.
For $(X,g)$ a Riemannian manifold and $\Delta : C^\infty(X) \to C^\infty(X)$ its Laplace operator, the wave equation on $X$ is the differential equation