Question 9 (10 points) Use the method of variation of parameters to find a particular solution of the differential equation.

Question 5 (10 points)  A tank contains 150 liters of fluid in which 10 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 5 L/min, and the well-mixed solution is pumped out at the same rate. Find the number of grams of salt in the tank at time .

Question 5 (10 points)  A tank contains 360 liters of fluid in which 40 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 6 L/min, and the well-mixed solution is pumped out at the same rate. Find the number of grams of salt in the tank at time .

Question 6 (10 points)  A 24-pound object stretches a spring 4 inches by itself. There is no damping and no external forces acting on the system.  The spring is initially displaced by 3 inches upward from its equilibrium position and given a velocity of 2 ft/sec downward.  Find the displacement at any time t. 

Question 9 (10 points)  Use the method of undetermined coefficients to solve the differential equation.

Question 10 (10 points)  Find the general solution of the given second-order differential equation.

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 2 (10 points) Find an implicit general solution for the first-order ordinary differential equation.  

Question 1 (10 points) Theorem (Existence and Uniqueness): Let be a rectangular region in the

Calcium carbonate, phosphates, and manganese may precipitate out of solution to form deposits on the ocean floor.