Slope Field Explorer
See the direction field of dy/dx = f(x, y) — then click anywhere to trace the solution curve through that point.
Click anywhere on the field to trace the solution curve through that point (Euler’s method, traced both directions).
① Answer
② Steps
③ Why it works
A slope field draws a tiny tangent segment at each point (x, y) with slope f(x, y) — no solving required. Solution curves must thread through the field following the segments, so you can see families of solutions, equilibria, and long-term behavior at a glance. Clicking traces one curve numerically with Euler’s method, stepping along the local slopes.