4. Solve the homogeneous linear differential equation y”’ – 2y” + y’ = 0.

State the function of the following sentences: Declarative, Imperative, Interrogative, Exclamatory. 1. Give me a few weeks to give you an answer. [Sentence1] 2. We hold a reading camp in the summer. [Sentence2]3. What time is the final exam? [Sentence3]4. I can’t believe it’s tomorrow! [Sentence4]

9. Use Laplace transforms to solve the initial-value problem:      y” – 4y’ = 3e-t, y(0) = 0, y'(0) = 0.

Both spider plots and tornado diagrams can be used to

2. Use an integrating factor to solve the linear differential equation 

A point on a wheel of radius 40 cm that is rotating at a constant 5.0 revolutions per second is located 0.20 m from the axis of rotation. What is the acceleration of that point due to the spin of the wheel?

7. Solve the differential equation y” + 9y = csc 3x.

A tennis ball bounces on the floor three times, and each time it loses 23.0% of its energy due to heating. How high does it bounce after the third time, if we released it from the floor?

1. Solve (1 + x) dy – y dx = 0 by using separation of variables.

In the figure, block A has a mass of 3.00 kg. It rests on a smooth horizontal table and is connected by a very light horizontal string over an ideal pulley to block B, which has a mass of 2.00 kg. When block B is gently released from rest, how long does it take block B to travel 80.0 cm?