ODE

Proofs that I’d like to learn:

• Existence, uniqueness, and interval of validity
  • Picard’s theorem
• Why 2nd order odes’s homogeneous solution is a family of two solutions: $C_1{y}_1(t)+C_2{y}_2(t)$

Resources

• Math 2080: Introduction to Ordinary Differential Equations.| Dr. Macauley
• Numerically Solving Ordinary Differential Equations (Brorson) - Mathematics LibreTexts
• ODEs: Introduction to Differential Equations
• MATH 8430: Fundamentals of ODE. | Julien Arino - Mathematical epidemiologist
• Introduction to ordinary differential equations | Roberto Monti