Math 107: Calculus II, Spring 2008: Midterm IPractice Exam II SolutionsSolutions1.(a) Find the general solution to the following separable differential equationdxdt=tx-t.(b) Find the specific solution to the differential equation from part (a) that hasx(0) =-1.(Write your answers in the formx(t) =. . ..)1
2. The giant panda population at timet(measured in years) is given by the functionP(t)(measured in thousands – i.e.P= 1means there are 1000 pandas).This functionsatisfies the following autonomous differential equationdPdt= (P-2)(10-P).(a) What are the equilibrium solutions to this differential equation?(b) Use the first derivative test to find the stability of the equilibrium solutions.(c) Sketch the solutions to this differential equation.