Sketch slope fields for first-order ODEs dy/dx = f(x,y)
Trace solution curves through given initial conditions
Identify equilibrium solutions and their stability
Develop intuition for qualitative behavior of solutions
Key Concepts
\( \frac{dy}{dx} = f(x,y) \)
Each small line segment shows the slope dy/dx at that point. Solution curves follow the "flow" of these segments.
Click anywhere on the graph to trace a solution curve through that initial condition.
Why It Matters
Slope fields let you visualize solutions to differential equations without solving them analytically. They reveal solution behavior, equilibria, and help develop qualitative reasoning critical for the AP exam.
Tags
slope fielddifferential equationsODEsolution curvesAP Calculus AB
ODEdy/dx = x − y
Curves0
Grid Density 15
Segment Length 0.6
Equation dy/dx =
Color Mode
💡 Click on the graph to trace a solution curve through any initial condition (x₀, y₀).
Quick Quiz
In a slope field, horizontal segments (slope = 0) indicate: