Problem $6.$ A researcher was studying a small forest with population of foxes and rabbits. After several years of observations they concluded that the population of rabbits oscillate around $1000$ rabbits and the population of foxes oscillates around $100$ foxes. To model that they wrote the population of rabbits as P$1=1000+$ y$1$ and the population of foxes as P$2=100+$ y$2.($a$)$ Pick which of the following four differential equations for y$1,$ y$2$ best models the above situation.