Slope Field Explorer
A first-order differential equation y′ = f(x, y) assigns a slope to every point of the plane — draw them all as small dashes and you can literally see the equation. This explorer renders the slope field for a menu of classic equations (linear, logistic, circular, oscillating) and lets you click anywhere to drop an initial condition: a solution curve is integrated through that point with Runge–Kutta in both directions, threading its way along the dashes. It is the picture that makes existence and uniqueness feel obvious.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- Each dash has slope f(x, y); solution curves must stay tangent to the dashes they pass.
- Distinct solution curves never cross where f is smooth — that is the uniqueness theorem in picture form.
- Equilibria appear as horizontal rows of dashes; solutions flow toward stable ones and away from unstable ones.
- Runs 100% in your browser — simulations are computed locally on your device.
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