Worksheet: 2nd-Order Linear Homogeneous Differential Equations with Constant Coefficients
In this worksheet, we will practice solving first-order differential equations.
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 .
Find the general solution for the following higher-order differential equation: .
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.
Find the general solution for the following homogeneous ordinary differential equation with constant coefficients: .