Cauchy Problem: Global vs Non-Global Solutions

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Discusses the Cauchy problem for ODEs with initial conditions and the importance of homeomorphism and Lipschitz continuity.

Covers the Cauchy problem, focusing on the existence and uniqueness of solutions to differential equations.

Explores equilibrium and stability of a vertical metronome system with springs.

Explores solving first-order homogeneous differential equations through variable changes and delves into the Bernoulli differential equation.

Covers the path integral representation of propagators for free particles and harmonic oscillators.

Covers the Cauchy problem in differential equations, focusing on initial conditions and their impact on solution uniqueness.

Covers the existence and uniqueness of solutions for differential equations.

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

Covers differential equations, including examples and unique solutions.