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

In this worksheet, we will practice solving first-order differential equations.

**Q1: **

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 .

**Q2: **

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

- A
- B
- C
- D

**Q3: **

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

**Q4: **

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

- A
- B
- C
- D