Ordinary Differential Equations
Explore first-order equations; linear equations and forcing; systems and phase space. Concepts and connections are available independently of video coverage.
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Integrating factors
An integrating factor turns a linear first-order ODE into a product derivative.
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Existence and uniqueness for ODEs
Continuity and suitable local Lipschitz conditions ensure a locally unique initial-value solution.
Separable equations
Separation places dependent and independent variables on opposite sides before integration.
Bernoulli equations
A power substitution converts a suitable nonlinear first-order Bernoulli equation into a linear one.
Characteristic equations
An exponential trial converts a constant-coefficient homogeneous linear ODE into a polynomial equation.
Equilibria and stability
Stability describes whether nearby trajectories remain close to or approach an equilibrium.
Knowledge connections
- Separable equations · Related · Map context
- Existence and uniqueness for ODEs · Related · Map context