I've got the following differential equation system:,
dU/dt = delta·dotD -lambda·U - kappa·U^2
dL/dt = (1-phi)·lambda·U + 1/4 ·kappa·U^2
being phi, delta, kappa, lambda, kappa some fixed parameters of the system, and where dotD (the derivative wrt time of a function D), which is defined a piecewise funtion:
dotD(t)=1/(3·T1)·DT for t in [0,T1]
dotD(t)=2/(3·(T2-T1-T))·DT for t in [T1+T,T2]
where T and DT are also known, and T1 approaches 0, and T2 approaches T1+T.
Setting the equation system in Maple and trying to solve it, gives a NULL result. However, trying to solve each piece separately seems to work fine.
Why is this?
Furthermore, taking limits for the [T1+T,T2] part (having solved each piece separately) yields an invalid limits point error. Ain't the possibility to take limits for both parameters at the same time?
This is the Maple worksheet: MaplePrimes_LQ_model_solve.mw