calculuas

A sack containing a liquid chemical is placed in a tank. The chemical seeps out of the sack at a rate of 0.1x litres per hour, where x is the number of litres of the chemical remaining in the sack after t hours. The chemical in the tank evaporates at a rate 0.2y litres per hour, where y is the number of litres of the chemical in the tank after t hours. If the sack originally contained 50 litres of the chemicalk, find differential equations for x and for y, and solve them. Find the greatest amount of chemical in the tank, and when this occurs.

(%i1) integrate(b*c*%e^(c*t)*sin(c*t),t);
(%o1) (b*%e^(c*t)*(c*sin(c*t)-c*cos(c*t)))/(2*c)