A more general and also complicated love between Romeo and Juliet is the IVP⎩⎨⎧R˙=f(t,R,J),J˙=g(t,R,J),R(0)=R0,J(0)=J0,wherefandgare two real functions dependent ont,R, andJ. Similarly, find conditions onfandgso that the IVP SYS. (14) has a solution. For example, a solution exists for IVP SyS. (14) wheref(R,J)=R(1−J)andg(R,J)=J(R−1)(this is also known as the Lotka-Volterra equations in Biology to model the interaction of two species). Give five specific examples of such IVPs without finding the exact solutions.