# Worksheet: 2nd-Order Linear Homogeneous Differential Equations with Constant Coefficients

Q1:

Find the general solution for the following higher-order differential equation: .

• A
• B
• C
• D

Q2:

The one-dimensional time-independent Schrodinger equation is given as

where is a wave function which describes the displacement of a single particle of mass , is the total energy, is the potential energy, and is a known constant. Since for the particle-in-a-box model, where , this second-order differential equation becomes

Find the general solution for this differential equation.

• A
• B
• C
• D

Q3:

Find the general solution for the following homogeneous ordinary differential equation with constant coefficients: .

• A
• B
• C
• D

Q4:

Consider the differential equation . Suppose that a student determined the solution to be . Based upon this information, is the student correct?

• ANo, the student should have determined that there is no solution.
• BNo, the student should have determined the solution to be .
• CYes, the student did not make any errors.
• DNo, the student should have determined the solution to be .