Examples:

  1. We will now solve the problem of rabbit and fox populations with initial conditions r(0)=100 and f(0)=100
    de1:=diff(r(t), t)=alpha*r(t)-beta*r(t)*f(t)
    de2:=diff(f(t), t)=-g*f(t)+delta*r(t)*f(t)
    eqnset:={de1, r(0)=100, de2, f(0)=100}
    solutions:=dsolve(eqnset, {r(t), f(t)})

    Maple Screenshot

    Note: This does not produce a solution because Maple can not find an analytic solution. If you do it with the ODE analyzer it tells you that you can not find a solution. In the next module you will learn about Numerical Methods to solve this problem.