Math 2250
Week 1 Quiz
Name and Unid:
Write your answer in the space provided. Show work for full credit.
1. (10 points) Verify that y(x) = 3e−2x is the solution to the following ODE
y 0 + 2y = 0.
Solution: Find y 0 :
y 0 (x) = −6e−2x .
Plug in:
y 0 + 2y = −6e−2x + 6e−2x = 0.
y(x) is a solution.
2. (10 points) A ball is thrown straight upward from the ground with initial velocity 96 ft/s.
Find the time it takes the ball to reach its maximum height. HINT: Take g = 32ft/s2 .
Solution: The acceleration is constant, i.e a = −g. Integrating, we have v(t) =
−gt + v0 . The ball reaches its maximum height when v(t) = 0:
−gtM + v0 = 0 ⇒ tM = v0 /g = 96/32 = 3s.
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