Differential Equations: Slope field and Euler's Method
Slope field: drag the corners P1 and P2 to adjust the size of the region
Euler's method: drag the red point A to change the initial condition, or enter its point coordinates.
Notice that it's up to you to ensure that the Function Equation is the solution to the differential equation.
If your function doesn't run along or parallel to the slopes in the field, then it must not be a solution!
If you have a correct solution curve, drag the red point A to various points along the curve to see how well Euler's Method does or does not approximate other values along the curve.
Can you develop any general observations of when Euler's Method tends to do a good job of approximating vs. when it does not do a good job?
2021, BC5 for APAC 2024
Version below used for presentation at AP Annual Conference 2024, reflecting Free Response Question AP Calculus BC 5 (and solutions).