the first question is a model which i set up on my own derived from question two .the conditons   a(0)=0  a(t1)=0  are something wrong ,i am sorry about that .now aims to solve question two.

lots of thanks to Robert Israel  !

the first example is a model derived from question two  set up on my own  . from Robert Israel's  analysis  i kow   the conditions a(0)=0  and a(t1)=0  are  wrong . the question two is an example from  textbook , the last three equations are nonlinear which are only  solved using numeric method.