Problem:
Using a slope field, find the graph of a solution of the differential equation

with the initial condition y(1)=1.

Visualization:
Using Slopes (from the University of Arizona):

  1. After starting up the program, you are prompted "Would you like some instructions?" Use the arrow keys to move to either Yes or No and then press .
  2. If you choose Yes then read the instructions and press when you are ready to proceed.
  3. Use the arrow keys to highlight Function Operations and press .
  4. Use the arrow keys to highlight Create Function and press .
  5. At the prompt, Enter numerator:, type
    2*x^2-x .
  6. At the prompt, Enter denominator:, type
    1 .
  7. At the prompt, Display graphics in a square region?, use arrow keys to highlight No and press .
  8. At the prompt, X coordinate of left screen edge :, type
    -2 .
  9. At the prompt, X coordinate of right screen edge :, type
    2 .
  10. At the prompt, Y coordinate of bottom screen edge :, type
    -1 .
  11. At the prompt, Y coordinate of top screen edge :, type
    3 .
  12. At the prompt, Initial x value :, type
    1 .
  13. At the prompt, Initial y value :, type
    1 .
  14. Use the arrow keys to highlight Plot Slopes and press .
  15. You will now see the coordinate axes.
  16. Press s to see the slope field:

  17. Press c to see the solution corresponding to the initial point (1,1):

    Press x or y to change the coordinates of the initial point.