Now lets say I give you a non-linear ODE that no-one can solve, but I say "'foo(x)' is the function which describes the solution to this ODE". It is a more or l

Now lets say I give you a non-linear ODE that no-one can solve, but I say "'foo(x)' is the function which describes the solution to this ODE". It is a more or less pointless statement, but all it means is that 'foo(x)' gives the curve that solves the ODE. Sounds like how we got Bessel functions, no?