Differential Equations: Slope field and Euler's Method
Slope Field: With "show corners" enabled, drag points P1 and P2 to adjust the size of the region. Option exists to show the numerically-generated solution curve through point A, which may be dragged to any location on the plane.
Euler's Method: Drag point A to change the initial condition, or enter its point coordinates in the input box.
Function Equation: Gives option to enter a function equation that is presumably thought to be a solution to the differential equation. Include a constant of integration "C" or "c" if desired. Alternatively, may be used to prove that entered function does not solve the differential equation if the graph does not run parallel to the slopes in the field.
If you have a correct solution curve, drag 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).