I was reading about calculus the other day, and for some reason I found out about Weierstrass function, a function that is continuous everywhere but differentiable nowhere.
Now, I do know there are some differential equation whose solution is continuous everywhere, but not necessarily differentiable everywhere (i.e., solution to Particle in a Box).
My question is, are there any differential equation whose solution is continuous everywhere but differentiable nowhere? Or is that impossible?