Question 5 (10 points) Use the method of variation of parameters to find a particular solution of the differential equation.

Question 8 (10 points)  Determine a suitable form for if the method of undetermined coefficients is to be used.  Do NOT evaluate the constants.

Question 8 (10 points)  Determine a suitable form for , if the method of undetermined coefficients is to be used.  Do NOT evaluate the constants.

Question 6 (10 points)  A 8-pound object stretches a spring 3 inches by itself. There is no damping and no external forces acting on the system.  The spring is initially displaced by 1 inch upward from its equilibrium position and given a velocity of 2 ft/sec downward.  Find the displacement at any time t. 

Question 6 (10 points)  A 16-pound object stretches a spring 8/9 feet by itself. There is no damping and no external forces acting on the system.  The spring is initially displaced by 6 inches upward from its equilibrium position and given a velocity of 1 ft/sec downward.  Find the displacement at any time t. 

Question 10 (10 points) A 48-volt battery is connected to a series circuit in which the inductance is henry and the resistance is 16 ohms. Determine the current if the initial current is zero.

Question 6 (10 points) Find the general solution (and a particular solution for the IVP) and determine whether there is any transient term in the general solution. where

Question 8 (10 points) A hot object at 200°C is cooling in a 30°C room and reaches 150°C in 8 minutes. When will it be 90°C?

Question 5 (10 points) Solve the Bernoulli differential equation:  

Question 9 (10 points) Use the substitution method to solve: