@Preben Alsholm Thank you...i really appreciate your time, input and patience...you are the man!!!

@Preben Alsholm I get it now. Finally i am done. Thanks. Can you advice on where or how i can get some formal training on using maple. I mean some form of structured learning

@Preben Alsholm i tried to add the following entries

but it do kept introducing erorrs. Please advice

@Preben Alsholm it worked.

thank you

@Preben Alsholm thank you for the response. I did not get them earlier. as u directed, i am reviewing the equations

@Carl Love you are correct...i didnt get this response either. i have found some issues with the equations i used and i am looking into it. Thanks

@Preben Alsholm hi, i was holding my breath in anticipation of your response to my post. I was kinda sad when i didnt get a response from you. I will be much oblidged if you can take some more time to help with my issue.

@Preben Alsholm thank you for your response. I did try all the lines and the solution was excecute. Thank you. I also change the plot range from 10^6 to .0000031 for t. The problem however is that the solution is not as expected. The equations are associated with a combustion reaction of Fuel(F) and Oxidant (O) to give Product (Pr) at varying temperature (T) and Pressure (P) . what is expected is that F and O will reduce with time and Pr will increade with time.

@bunmipopoola the solution should look like this

@bunmipopoola the solution should look like this

thank you for your response. Now i am making some progress.

the equations would not solve

sol := dsolve(`union`(sys2, ics2), numeric);
print(`output redirected...`); # input placeholder
Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)
proc(x_rkf45)  ...  end;
odeplot(sol, [[t, P(t)]], 0 .. 10^(-6));
%;
Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

odeplot(sol, [[t, F(t)]], 0 .. 10^6);
%;
Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

odeplot(sol, [[t, T(t)]], 0 .. 10^6);
%;
Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

I should mention that the equations are stiff

thank you for your response. Now i am making some progress.

the equations would not solve

sol := dsolve(`union`(sys2, ics2), numeric);
print(`output redirected...`); # input placeholder
Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)
proc(x_rkf45)  ...  end;
odeplot(sol, [[t, P(t)]], 0 .. 10^(-6));
%;
Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

odeplot(sol, [[t, F(t)]], 0 .. 10^6);
%;
Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

odeplot(sol, [[t, T(t)]], 0 .. 10^6);
%;
Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

I should mention that the equations are stiff