Nobody wants to have to type in all your code.It's impolite of you to expect an answer without providing the code to reproduce.

People here generally like users to post (complete) code as Maple code instead of just images,pdf or TeX, so they can copy-paste it(Use green arrow and upload worksheet). It makes it convenient for them and more likely you will get someone to help you.

Maple 17: release date is: March 13, 2013.

Maple 2017: release date is: May 25, 2017

During these 4 years int command it has been improved and is more powerfull.

@mwahab 

With Maple 2020.2 works fine.Maybe is version issue.

See attached file.

solution_bug_1_ver2.mw

Looks like a bug.

Submit Software Change Request.

@Nick_99

Maple can compute only 5.1268948 > t >0 because singularity.

I update the answer.

From Help pages:

The discont option is not available in the 3-D case.  In this situation, it is recommended that you divide the plotting ranges into subranges to avoid the discontinuities, generate the individual plots and then combine them using the plots[display] command.  The view option can be used to control the ranges in the final display.
 

@Carl Love

An example: 

DSolve is symbolic solver.

NDSolve is numeric solver.

What value have c parameter? Or is c(t,x) ?

For k(x)  function using FourierTransform it just: k(x)= (1/4)*sech((Pi*x)/2) .

@graleo 

If I change to:  u2(x, 1) = 1 ,Maple give me a error messages: "unable to handle elliptic PDEs", that's mean Maple can't solve.

See for more info: https://www.mapleprimes.com/questions/227556-Elliptical-PDEs

@graleo 

Please post the equations, in copy-and-pastable Maple format. It is unrealistic to expect people to re-key them.

It is impolite to expect other people to have to type in your equations for you.

@Axel Vogt 

Looks like:

sum(2^(2*j)*(-2*j + 1)^(-j)*GAMMA(-1/2 + j)/sqrt(Pi) - 2^(2*j)*(-2*j + 1)^(-j)*GAMMA(-1/2 + j)*GAMMA(j + 1, (-1/2 + j)*ln(2))/(sqrt(Pi)*GAMMA(j + 1)), j = 0 .. infinity);

evalf(%);

0.690239719

With no hope for closed-form.

Please post the equations, in copy-and-pastable Maple format. It is unrealistic to expect people to re-key them.

It makes it convenient for them and more likely you will get someone to help you.

Please post the equations, in copy-and-pastable Maple format. It is unrealistic to expect people to re-key them.

@vv