$3.(25$ points$)$ The equations are given as:

y $001=$ y$1+2$y $02$ y$1+$ D$1$ y$1$ D$2$ y $002=$ y$22$y $01$ y$2$ D$1$ y$2$ D$2$ D$1=(($y$1+)2+$ y $22)3/2$ D$2=(($y$1$ $)+$y $22)3/2$ Use parameter: $=0\mathrm{.}012277471,$ $=1,$ y$1(0)=0\mathrm{.}994,$ y $01(0)=0,$ y$2(0)=0,$ y$02(0)=2\mathrm{.}0015851063790825.$ It is known that the solutions would become periodic, i$.$e$.,$ the object will following a certain orbit. When t $=17\mathrm{.}065211656$ it would complete one full round of its orbit. $1.$ Write a program that would solve the system with the classical $4$th order Runge$-$Kutta method, but reduce the step number to $6000.$