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: .