Concept explainers
Recall that a family of solutions includes solutions to a differential equation that differ by a constant. For the following problems, use your calculator to graph a family of solutions to the given differential equation. Use initial conditions from y(t = 0) = -10 to y(t = 0) = 10 increasing by 2. Is there some critical point where the behavior of the solution begins to change?
54. In the preceding problem, if the initial velocity of the ball thrown into the air is a = 25 ft/s, write the particular solution to the velocity of the ball. Solve to find the time when the ball hits the ground.
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