Problem 4.1: Find the GS (with one given solution y1(x) = x2) of x3y' = x4 x2}! + 23/2 Problem 4.2 ( Textbook: Probfem 2.3.10 on P91): Suppose that the sh population P(t) in a lake is attacked by a disease (such as human being who eats them) at time t = 0, with the result that the fish cease to reproduce (so that the birth rate is [3 = 0) 1 and the death rate 6 (deaths per week per fish) is thereafter proportional to PT. If there were initially 10,000 sh in the lake and 199 were left after 19 weeks, how long did it take for the lake to contain 0 fish? Can you change the "199\" to a different number such that the sh count never changes with time? To what number ifso