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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Exact differential equations
A differential expression is exact when it is the differential of a potential function on the domain.
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Bernoulli equations
A power substitution converts a suitable nonlinear first-order Bernoulli equation into a linear one.
Existence and uniqueness for ODEs
Continuity and suitable local Lipschitz conditions ensure a locally unique initial-value solution.
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.
Initial value problems
Initial data select solutions of a differential equation when existence and uniqueness conditions hold.
Knowledge connections
- Existence and uniqueness for ODEs · Related · Map context
- Bernoulli equations · Related · Map context