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Mathematics · Glossary

What is Differential equation?

Definition 26.1 High School Mathematics · Chapter 26 — Differential Equations

A differential equation is an equation whose unknown is a function yy, involving yy and its derivatives. A solution on an interval II is a differentiable function satisfying the equation at every point of II.

The equation y' = y prescribes a slope at every point of the plane (gray segments). The solutions C x — here C = 1 (blue), C = 0.3 (red), C = -0.5 (orange) — are exactly the curves that follow this field of slopes.
The equation y′=yy' = y prescribes a slope at every point of the plane (gray segments). The solutions CexC\eu^{x} — here C=1C = 1 (blue), C=0.3C = 0.3 (red), C=−0.5C = -0.5 (orange) — are exactly the curves that follow this field of slopes.
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