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1. Solve the following first-order differential equation: y' - 3y = e3t
2. Suppose a baseball with a mass of 0.15 kilograms is thrown vertically upward with an
initial velocity of 35 m/s. Assume gravity is -10 m/s^2 and air resistance is b = 0.03.
How high does the baseball go?
You can assume the initial height is 0 meters.
Use the formula: ma = mg - bv
[First, input the values given into the formula above. Second, DERIVE the equations for
the velocity, v(t) and the position, s(t). It is NOT enough to use the equations from
Nagle's book, thirdly, figure out how high the baseball goes!)
3. Solve the following second-order differential equation:
4y" – 4y' + 5y = 0, y(O)=1, y'(O)=-11/2
4. Consider the differential equation: y" + 2by' + y = 0 where b is a constant. Describe
how the solutions to the equation change as b varies. In other words, there are three
solutions depending on the value of the parameter b. Write these three possible
solutions.
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