Is there any Good library for solving differentiation equations using differentiation operator?

Question

Good library for solving differentiation equations (not only 1rst order) using differentiation operator?Better written in C/C++/PHP/C#/Actionscript/Javascript

Answer 1

(1) Generic analytic ODE solver is not possible.

(2) If you're given an n-th order ODE you can convert it into n 1st order ODE, e.g.

y'' + 2y' + 3y + 4 = 0

now let z = y', you've got a coupled 1st order ODE:

z' = -2z - 3y - 4
y' = z

(3) For C, try GSL: http://www.gnu.org/software/gsl/manual/html_node/Ordinary-Differential-Equations.html.