What better use for a computer algebra system than a problem whose solution you know intuitively, and for which the paper-and-pencil work feels too daunting to start? Here’s a problem that exploits what we know about the solutions of damped driven oscillators, making use of the usual ODE capabilities in Maxima, together with a nonlinear solve with find-root at the end.
Here’s an easy start-to-finish test run for solving an ordinary differential equation in Maxima. The keys are: the ‘diff(y,x) form of the derivative, the commands ode2 and ic2. For verifying the solution: ev and rhs.
I’ve been talking to my differential equations class about linear combinations of linearly independent solutions for higher order linear, constant-coefficient, homogeneous equations. Here’s how it looks when we let Maxima do the heavy lifting.