Methods for Differential Equations Physics Students Need to Know

Learn five powerful methods for solving differential equations essential for physics students: substituting an ansatz, using energy conservation, making a series expansion, applying the Laplace transform, and utilizing Hamilton's equations. Explore these techniques through the F=ma equation for a simple harmonic oscillator, gaining valuable insights applicable to more complex physics problems. Discover how to visualize solutions as flows on phase space and solve equations using matrix exponentials, preparing you for advanced concepts in your physics studies.

Introduction
The equation
1: Ansatz
2: Energy conservation
3: Series expansion
4: Laplace transform
5: Hamiltonian Flow
Matrix Exponential
Wrap Up