Math 107, Fall 2006: Midterm I Practice Exam I Solutions1.(a) Find the general solution to the differential equationdydt= 3t2+et.(b) Find the specific solution to this equation that has the initial conditiony(0) = 3.
2.Consider the autonomous differential equationdydt=g(y)whereg(y) = (1-y)y.(a) Find the equilibrium solutions of this equation.(b) Use the first derivative test to classify the stability of these equilibria.(c) Sketch the solutions to this differential equation.