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Unformatted text preview: Final Exam Math 220 December 12, 2005 Name: Directions: Show all your work on these papers, using the back if necessary, and circle your answers if thats appropriate. The Laplace transforms you need are on the blackboard. Remember that if youve made it this far, you can do all of these problems. 1. (10 pts) Solve the inital value problem (IVP) x + 1 t x = cos( t ); x ( 2 ) = 1 2. (10 pts) The population N of a certain species is modeled by the differential equation dN dt =- ( N- 10)( N- 100) . Find the equilibrium points and classify them as stable or unstable. Plot some approximate representative solutions N ( t ) for initial conditions lying between 0 and 150. 3. (15 pts) Find the general solution to x 00- 3 x +2 x = 2 sin(2 t ). Use the method of undetermined coefficients for the inhomogeneous equation. Identify the transient and steady-state solutions. 1 4. (10 pts) When a 1 gram mass is attached to a spring, it displaces the spring 10 cm from its equilibrium position.equilibrium position....
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