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Differential Equations Lab
Slope Fields & Phase PortraitsClick anywhere on the canvas to plant an initial condition and watch the solution curve unfold.
System
Controls
Show Equilibria
Current System
dy/dx = ry(1 − y/K)
Models population growth with a carrying capacity K. Solutions S-curve toward K.
Initial Condition
Click on the canvas to drop a solution curve.
How to Read This
- • Arrows show the direction & speed of change at each point.
- • Glowing trails are integral curves — exact solutions through your chosen point.
- • Circles (when visible) mark equilibrium points where dx/dt = dy/dt = 0.
- • Green = stable (attractor), Blue = center (orbit), Red = unstable (repeller).
✦ Click to plant an initial condition