Unformatted text preview: Sample questions for Exam 2
1. Find the general solution to the following equations: a. y + 2y + 10y = 0 b. y - 4y - 5y = 0 c. y + 6y + 2y = 0 d. y + y + 0.25y = 0 e. y - 6y + 25y = 0 f. y + 8y + 15y = 0 g. y + 2y - y - 2y = 0 h. y - 2y + y = 0. i. y - 3y + 3y - y = 0. j. y - 3y - 4y = 0. 2. Solve the initial value problem y + 4y + 4y = 0, 3. Find the general solution to y - 2y + 17y = e3t + 1. 4. Find the general solution to y - 2y - 8y = te4t + 3et . 5. Find the solution to the initial value problem y + y - 2y = 5e3t , 6. Find the general solution of y - 2y - 3y = -5 cos t + 6e-t 7. Consider the equation 8y + y + 8y = 0, y(0) = 2, y (0) = 0, describing a spring oscillator. Is the solution of this equation critically damped, underdamped, or overdamped? Make a SKETCH of the solution. Now consider, 8y + by + 8y = 0. Name a specific value of b which causes this "spring" oscillator to display each of the other two types of motion. Make a sketch of each of these other two solutions, y(t). Which of these three types would you like to have in your cars shock absorber system? How about in the spring which closes your back screened door? Why? 1 y(0) = 4, y (0) = 6. y(0) = 3, y (0) = 1. ...
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- Fall '08
- Equations, Boundary value problem, Shock absorber, general solution