> PDEs are really useful if you are in the rare domains where they are useful. Aside from ‘rare’, this seems at best vacuously true. > But most PDEs don't hav

> PDEs are really useful if you are in the rare domains where they are useful. Aside from ‘rare’, this seems at best vacuously true. > But most PDEs don't have even have closed form solutions for non-trivial boundary conditions. So unless you are a physicist or something adjacent, no, no you really don't need to know these. As others have said, while your first sentence is surely true, the latter doesn't follow from it (and I would argue isn't true—but it depends on how you define adjacency). There are lots of things one can usefully do with an equation besides finding a closed-form solution. (For an ODE example, the classical predator–prey model does not have a nice closed-form solution, but is still plenty useful.)