Is there any way that Maple only solves first 9 equations and then substitutes the resluts to the last equation at each instant?
Like I said, I already did solve it for only the first 9 equations. Doing so, each "instant" would take on the order of 53 minutes of CPU time. So if the integration uses, say, 200 evaluation points, then that could take a week or more. (Although there may be a "learning" effect where subsequent evaluation points take less time.)
Update: In addition, without last ODE, by using "eliminate" function in order to remove lambda 1 and lambda 2 from the equations, Maple can solve first 9 ODEs without any errors or warning.
Like I said, the dsolve itself ran fine in 22 seconds. It is using the results of the dsolve that takes a lot of time.
There's a chance that increasing the error tolerances and settings Digits to, say, 4 will make it run significantly faster. I don't have much hope for this approach though. It might be possible to simplify the equations after the eliminate and before the dsolve. And it might be possible to apply a code optimizer like codegen[optimize] to the procedure that dsolve returns.