kosovtsov said:There are three function in your system of two ODEs. If a(t) and f(t) are unknown functions then you can proceed in Maple by following way
AN:=dsolve({ec1,ec2},{a(t),f(t)});
ans:={op(1,op(1,AN)),simplify(eval(subs(op(1,AN),op(1,op(2,AN)))),symbolic)};
odetest(ans,{ec1,ec2});