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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. Page 2