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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Variation of parameters
Variable coefficients multiplying homogeneous solutions construct a particular solution of a forced linear ODE.
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Characteristic equations
An exponential trial converts a constant-coefficient homogeneous linear ODE into a polynomial equation.
Laplace transform
An integral transform converts time-domain derivatives into algebraic relations under convergence conditions.
Bernoulli equations
A power substitution converts a suitable nonlinear first-order Bernoulli equation into a linear one.
Equilibria and stability
Stability describes whether nearby trajectories remain close to or approach an equilibrium.
Exact differential equations
A differential expression is exact when it is the differential of a potential function on the domain.
Knowledge connections
- Characteristic equations · Related · Map context
- Laplace transform · Related · Map context