ANSWERS: 1

I think anyone who says he or she can solve a(n arbitrary) differential equation doesn't know very much about differential equations. That said, I love trying to solve differential equations. Out in the wild (not at the university), I'd guess that about half of the differential equations I encounter are trivially solvable (ordinary, linear, homogeneous), and most of the other half are impossible to solve by any method that doesn't involve FEA or at least RungeKutta. The small percentage that are nontrivial, analytically solvable, and model some realworld application are pretty exciting, though.
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