I have a system of two ODE's. One is of the form dT/dt=a*(dc/dt)-b, where a and b are constants. The other is of the form dc/dt=-(c^2)*d*exp(j*(1/T-1/k)), where d,j, and k are constants. I need to find the maximum value for T. I can solve dT/dt via the separation of variables method to get and expression T=f(c,t). I then substituted this expression into dc/dt=f(c(t),t) and solved it numerically in Maple. How do I substitute the values of c(t) obtained in Maple into T=f(c,t) and find the maximum? Or is there a better method? I tried solving this as a system of two ODE's but since one ODE is nested in the other I could figure out the correct syntax.
Thanks for the help.