$5.$ Modify the Fortran main program discussed in this course in order to solve the following

nonlinear problem.

Bioremediation involves the use of bacteria to consume toxic wastes. At steady state, the

bacterial density, x$,$ and nutrient concentration, y$,$ satisfy the equations,

xy $$ x$(1+$ y$)=0,$xy $+($ $$ y$)(1+$ y$)=0,$

where and are parameters that depend on various physical features of the system; for

this problem use $=5$ and $=1.$ Find one solution to this problem with a non$-$zero

bacterial density and one solution to this problem for which the bacterial population has

died out. HINT: For the first case, start with x $=1$ and y $=0\mathrm{.}5.$ For the second case,

start with x $=0\mathrm{.}3$ and y $=0\mathrm{.}5$