Differential Equations proficient (only). Please see the question below and thank you ahead of time.

38. Consider the cascade of two tanks shown in Fig. 1.5.5. with Vi = 100 (gal) and V2 = 200 (gal) the volumes of brine in the two tanks. Each tank also initially contains 50 lb of salt. The three flow rates indicated in the fig- ure are each 5 gal/min, with pure water flowing into tank 1. (a) Find the amount x () of salt in tank 1 at time I. (b) Suppose that y() is the amount of salt in tank 2 at time /. Show first that dy 5x 5y 100 200 and then solve for y(), using the function x (t) found in part (a). (c) Finally, find the maximum amount of salt ever in tank 2. Tank 1 Volume V1 Amount I Tank 2 Volume Va Amount y FIGURE 1.5.5. A cascade of two tanks