2. (07.01 MC) Which step is necessary in verifying that InB + 3 = -3t is a solution to dB =-3B? dt 1 dB B dt -3 O [ (InB +3)dB = [-3t dt O elnB + e3 = e-3t O edB = -3dt 3. (07.01 MC) A 3-kg object in motion is experiencing a force, F, that is proportional to the object's mass times the rate of change of its velocity, v, with respect to time, t. What differential equation represents this dynamic? (6 points) OF =3 dv OF = 3v OF = 3t O F =3 dav off 2All changes saved 4. (07.02 HC) Consider the differential equation y = x2(y + 2). dx Sketch a slope field for the given differential equation on your paper for the domain [-3, 3] and the range [-3, 3]. Part A: List five coordinates and the corresponding slope of their segments. (5 points) Part B: Using the slope field that you drew, describe all points in the xy-plane for which the slopes are negative. (5 points) D5. (07.02 MC) The differential equation y ' = 3x will produce which of the following? (6 points) O A slope field with rows of parallel tangents A slope field that does not have rows or columns of parallel tangents A slope field with parallel tangents along the diagonal A slope field with columns of parallel tangents 6. (07.01 HC) For the differential equation Y = ex _ 3x3: dx Part A: Find a general solution. Show all your work. (5 points) Part B: Verify the solution. Show all your work. (5 points)7. (07.03 MC) A function f is a solution to the differential equation f'(x) = 1 - 2x + y with an initial condition of f(-1) = 2. n 0 1 2 Xn -1 -0.8 -0.6 yn 2 ? ? Use Euler's method with a step size of 0.2 to complete the table of approximate solutions. (6 points) O y1 = 3 and y2 = 4.12 O y1 = 3 and y2 = 3.03 O y1 = 3.5 and y2 = 5.27 O y1 = 3.5 and y2 = 5.62