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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Second-order linear ODEs
A second-order linear ODE combines a function and its first two derivatives linearly.
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Characteristic equations
An exponential trial converts a constant-coefficient homogeneous linear ODE into a polynomial equation.
Ordinary differential equations
An ODE relates an unknown function of one variable to its derivatives.
Systems of ODEs
Coupled differential equations describe interacting state variables.
Undetermined coefficients
A forcing-compatible trial form finds particular solutions of suitable constant-coefficient linear equations.
Bernoulli equations
A power substitution converts a suitable nonlinear first-order Bernoulli equation into a linear one.
Knowledge connections
- Characteristic equations · Related · Map context
- Undetermined coefficients · Related · Map context
- Ordinary differential equations · Related · Map context
- Systems of ODEs · Related · Map context