Thank you so much @mmcdara 

@Carl Love Thank you

But what I don't understand why it's working fine in maple 2015 and get stuck in maple 2020?

Thank you so much @Preben Alsholm . 
 I add these two lines and it get stuck again in polarplot, is there anything to add or change?

fcty := RootOf(T, r);
polarplot(fcty);
 

mpprime.mw

@nm Thank you, I'll look for it

Thank you so much @dharr 

Thank you @Mariusz Iwaniuk

Thank you @Carl Love 

I am exciting to see your answer

Thank you @Preben Alsholm , I like your answer .

But for other equation the singularity will show up , and we can’t change the form of equation , so for that if it's possible  I  need a conditional if to re-solve the equation for example if it's a singularity must return and solve it ( dsolve ) and so that , I hope I have clarified the situation.

Algorithm

Random coefficient

Dsolve

Calculate eng

If eng = singularity

Return and dsolve

Else, end if

thank you 

Thank you @J4James ,

but i steal have probleme whene i change the last condition from 70 to 100 

psi(0.174568e-1) = 100, i get the flowing error ;

Error, (in dsolve/numeric/ComputeSolution) Newton iteration is not converging
 

best regards 

thank you Mr.@Preben Alsholm 

i will look for other way 

Best regards!

Thank you for your answer Mr.@tomleslie 

i defined the parameters but the problem still not solved 

Download Fourier_TRAns_MAPLEprime.mw

Thank you

thank you for your answer , but it's not work with dsolve 

Hi

Good idea 

thanks :)

Thank you very much 

how i can plot these solution ?