@Preben Alsholm 

Ohh...I know what you mean.

Sorry, this is my mistake. Actually, I simplify the equation, the original equation may not be this result. But according to what you stated, there are only 3 roots in this interval, fsolve found 4 and Analytic found 7?

@Markiyan Hirnyk 

Sorry...would you please explain in detail?
Actually, I don't very understand what you want to say...
I understand you use two ways to prove there are only seven roots of this function in these interval and plot real part and imaginary part seperately. But what is the relationship between them?

@Carl Love 

In my opinion, because real part and imaginary part of complex value are closure, if the real part of function intersect with y axis in 6 positions, there will be al least 6 complex values answers in these position which can make the real part into 0. But it seems that Analytic didn't found some of them?

Am I wrong?

@Alejandro Jakubi 

According to your answer, may I say that the answer is correct, because the pde is recognized by pdsolve. But there is a bug in the procedure of pdsolve, so it returns the unexpected result. 

BTW, does Maple 18 now can solve elliptic PDEs?

@Preben Alsholm 

Thanks your help, I just want to test the command pdsolve.

@Preben Alsholm 

OK, I see.

Thanks for your explanation in detail.

@Preben Alsholm 

Sorry, Would you please explain more clearly? I have a little confusion.

If D(y)(x)=f(x), y(x)=int(f(x),x)+C, where C is the constant., isn't it?

In some case, Maple can return the "general solution", for example:

@Carl Love 

Yes!! Thank you very much!!

And sorry for not explaination very clearly, English is not my native language.

@Carl Love 

Thanks for your suggestion.

I've noticed that the sum of R2 can be easier got al followed,

FYI.

@Kitonum 

Thank you for your advice in detail :)

@Carl Love 

OK, I think I have find the solution. The look option and upvector option is what I want. I lose them from the help page.

Thank you for your kindly help :)

@Carl Love 

I tried to use your approach to zoom the plot but encountered some problems.

First, it seems that the view angle will change automatically with different plots and Sometimes the plot will disappear as time goes, even I just zoom the plot along the z-axis. And I don't know how it was and how to lock it. For example,

viewpoint_test.mw

In this mw, there are no different in the viewpoint option between plot a1 and plot a2, but there is an oblique angle in the plot a1. And both of two plots will disappear after the 26th frame.

Second, is it possible to realize the translation? In the sample you mentioned earlier, I can zoom the plot on origin point along the z-axis. But if I want to translate the plot along the x-y plane, how can I do it? I tried to modify your sample such as [location= [seq([10*k, 0, 0], k= 100..10,-1)]], but the viewpoint will rotate.

@Carl Love 

Very great idea!

Thank you for your advice!

Thank you for your kindly help :)

@mehdi jafari 

Thank you very much!