You will need a basic calculator but you cannot use a graphing calculator.
Test 2 covers sections 3.1-3.8, although ealier topics may arise within Chapter 3 problems.
You should be able to find linearly independent real valued solitions to second order homogeneous linear differential equations with constant coefficients.
You should know how to find particular solutions in the nonhomogeneous case.
You should know how to solve Euler Equations.
You should know how to use the reduction of order method to find a second solution given one solution.
You should understand linear independence and dependence and the Wronskian.
Understand where, what domain, a solution is valid.
There will a word problem involving a mass spring system.
Be able to handle differential equations with discontinuous coefficient functions.
Anything in Chapter 3 is fair game.
Here is a link to some old tests: Old Tests.