• 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 Runge-Kutta. The small percentage that are non-trivial, analytically solvable, and model some real-world application are pretty exciting, though.
  • Did you have an equation to solve? If not, here's my favourite easy one... ready? Assume A is constant with respect to x and t: dx/dt = A x

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