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Unformatted text preview: Introduction to dfield , pplane and fplot It might be reasonable to expect that if two solutions of a differential equation which start close together, then they should stay relatively close together. We can investigate the behavior of solutions using the routine dfield . (1) Use dfield 7 and the “Keyboard Input” feature to plot the solution to the differ- ential equation y = y 2- 2 t with y (0) = 0 . 9185 . Now using the “Zoom In” feature, approximate y (3 . 2) to within 2 decimal places. (2) Erase all solutions. Now use dfield 7 and the “Keyboard Input” feature to plot the solution to the differential equation y = y 2- 2 t with y (0) = 0 . 9184 (instead of y (0) = 0 . 9185). Use the “Zoom In” feature to approximate y (3 . 2) to within 2 decimal places. Is this approximation close to the approximation in (1) ? (3) Erase all solutions and using dfield 7 plot the two solutions to: y = y 2- 2 t y (0) = 0 . 9185 and y = y 2- 2 t y (0) = 0 . 9184 on a single graph. This shows the solutions start close. Do they remain close ason a single graph....
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- Spring '08
- Boundary value problem