Solving 40 nonlinear algebraic equations can take considerable time.

Thanks for your advice. I am now trying to use NDSolve. It's indeed much faster than using DSolve. But I've encountered another problem. For 6 second-order ODEs with 12 boundary conditions, I can obtain the exact symbolic solutions in relatively less time by using DSolve. Then I plotted the first derivative of the symbolic solutions, from which I got the right graph. But when I used NDSolve to solve the same problem, I got nothing after I plotted the first derivative of the numerical solutions. Why so? Besides, the graph of the symbolic solutions is the same as the graph of the numerical solutions. Then why the graphs of the first derivative of the two solutions are totally different? Looking forward to your reply. Many thanks!!

Yes. Sorry, my fault. Now I know how to ask questions. The most efficient way of asking for help is uploading the problematic code, rather than describe the problem with empty words. Anyway, many thanks for your help and patience! :-)

I would never jump into a complicated problem without first trying out smaller similar problems. Ask yourself how long does it take to solve for a fifth, fourth, third, and half of that many conditions and estimate the time necessary to solve the whole number of conditions. The estimate won't be exact, but it should tell you if your talking hours, days, or weeks.

You can also time out other approaches as you make the problem grow and see how much time you could save on the big problem by using them.

Boundary value problems are much tougher than initial value problems. You may wish to try quasi-linearization, an iterative approach, rather than the built-in method, if you are looking for a numerical solution.

http://library.wolfram.com/infocenter/Conferences/368/