@mmcdara 

I thought that fsolve could give all numerical solutions before, but I did not think that fsolve could only give one. Later, I obtained many results after using solve, including the desired solution. Thank you for your guidance.

@Scot Gould 

I can't solve a couple after I wrap it in []

@acer 

First of all, thank you very much for your very organized reply. At first, I thought Rootof could give roots of all ranges, but I didn't realize that roots between 0.96-1 were not in this range.
Secondly, the solution of this root is really out of order, and my understanding of the solution of the root is wrong.
Finally, what if you want to draw an image that uses Rootof to solve for the maximum root and the second positive root by 3 times?
fuxian2.mw

@acer 

In this program you wrote, the index is used for indexing, but the order of his index is from small to large, so that it can not guarantee that the solution is the corresponding root of the formula - the middle is broken, and the two images on both sides are respectively corresponding to which one?

@acer 

This method has opened up a new way for me. I used to think that solving the function value can better draw the image, but I did not expect the rootof method to be so useful.But why does the middle section have no root? Is it because you can't get it?

@dharr 

Thank you, I have since tried some direct dsolve solutions with the same results as convertsys.And then I'm going to go straight to dsolve.

@C_R 

Sorry, I saw this error after not able to solve, originally thought is not called the Jacobi function package, but after the call still appeared this error

@C_R 

Thanks for your guidance and understanding that global variables cannot be directly replaced with local variables. I saw above that you said there was a problem with this Jacobian matrix. Can you elaborate?

@C_R 

@C_R 

Thanks, (tan(tehta))^2=-1 has no Angle correspondence. Combined with the actual situation of the problem, it is found that theta has little influence on the dynamic response. After solving a and c, I can estimate the result。Sincerely thank you for your approach, I learned a new method to solve this question.I find my maple ability is too poor, I would like to ask you what maple books recommend?

@C_R 

Learn the code you wrote and feel pretty good, but find that plugging a1 and c1 into secular7[1] is not the same as solving theta3 in secular7[3].

@Carl Love 

Thank you for your reply, using your method can indeed jump the singularity and continue to solve, but there are still many singularity points later, and the distance between the two singular points is getting closer and closer, I would like to ask why?

solve826.mw

@mmcdara 

Thank you for reminding me. I did not realize that gamma has a built-in function before. I have modified gamma

solu := dsolve(eval({ics, couple[]}, gamma = gamma__1), [eta(t), varphi(t), V(t)], output = procedurelist, numeric, maxfun = -1)

solve826.mw

@Carl Love When this method is used, the same command is used, but the error will always be reported. Why is this?

solve826.mw

@C_R I think it is more reasonable to solve the problem in this way