Midterm 3: Math 30, 11/19/07
5 pts 1) Find the length of the curve. Give the final number for full credit.
()
10,4 2/1
2<<−= xxy
5 pts 2) Find the area of the surface obtained by rotating the curve about the x-axis.
5 pts 3) Find the solution of the differential equation xy
dx
dy
x=+ )1( 2 that satisfies the initial
condition . Solve for y explicitly for full credit.
1)1( =y
5 pts 4) A bacteria culture grows at a rate of P
dt
dP
λ
=.
a) Find the solution for P(t) given the initial condition P(0) = Po ( You can guess the
solution but show that it satisfies the differential equation)
b) How long does it take for the initial population to double?
5 pts 5) A function y(t) satisfies the differential equation. 234 3512 yyy
dt
dy +−=
a) Find and plot equilibrium points
b) Determine whether equilibrium points are stable or unstable (or perhaps something
else).
Extra Credit(5 pts)
Solve the differential equation.