@Carl Love I have already calculated by hand the analytic solution, but it is the graphic solution which I need to analyse for my work. 

@Preben Alsholm I did not know the "convert/heaviside" command, and I've read the help page but still don't really understand it, and what is surprising is that the graph that what your work gives is very different from all the other ones, but closer to what I was hoping to obtain. Could you please rapidly explain? 

@Markiyan Hirnyk Thank you for your answer, however I have a small synthax problem with odeplot, I can't find how to choose the range of the y axis, although it is not a boundary value problem.. 

@Markiyan Hirnyk Thank you for your answer, however I have a small synthax problem with odeplot, I can't find how to choose the range of the y axis, although it is not a boundary value problem..