Not sure if differential equations really matter? I promise you, they do. There's a decent web feature called "17 Equations that Changed the World." Not all of the examples are differential equations, but a few are:
- The wave equation
- The Navier-Stokes equations for fluids
- Maxwell's equations for electromagnetism
- Schrodinger's equation for quantum states
- The logistic model for population growth (not technically a differential equation, but close)
- The Black-Scholes model for pricing financial derivatives
- Read the course syllabus.
- Read the group work policy.
- Read the online community guidelines.
- Read the problem set guidelines.