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First-Order ODE — Animated Explanations
Getting Started
Why Differential Equations?
A First Equation — y′ = y
Original Animations
A First Equation — y′ = y
Why Differential Equations?
Isoclines & Nullclines — the Paraboloid
Linear Isoclines — the Plane
Cubic Isoclines
Existence Region vs Solution Domain
Trapped Between Solutions
Orthogonal Families
Envelope of a Family
Singular Solution — Envelope
Stitching Solutions
Isoclines & Direction Fields
Isoclines and Nullclines
Example 1 — Paraboloid Isoclines
Example 2 — Linear Isoclines
Example 3 — Cubic Isoclines
Initial Value Problems
Existence-Uniqueness Domain vs. Solution Domain
Stitching Solutions of an ODE
Envelopes & Orthogonal Families
Envelope of a One-Parameter Family
Orthogonal Families
Singular Solutions
Singular Solutions — Definitions
Singular Solutions — Example