## 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)=*R*0,*J*(0)=*J*0,where*f*and*g*are two real functions dependent on*t*,*R*, and*J*. Similarly, find conditions on*f*and*g*so that the IVP SYS. (14) has a solution. For example, a solution exists for IVP SyS. (14) where*f*(*R*,*J*)=*R*(1−*J*)and*g*(*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.

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