Find the myequation of the curve that passes through (1, D] and whose slope at any point on the curve is equal to 4 times the m coordinate of that point. yzAzB+C,whereA: ,B: ,andC: Solve the differential equation using the technique of separation of variables y I + 212 dz _ ya Find the solution for which y = 6 when I = 0. y Z Use separation of variables to nd the solution to the differential equation of 3\" = H2, alt subject to the initial condition 11(0) : 2. u{t) = Falling-Body Problem Near the surface of the earth, the acceleration of a falling body due to gravity is 32 feet per second per second, provided that air resistance is neglected. If an object is thrown upward from and initial height of 1000 feet {Figure 2, Section 3.9, Example 3) with a velocity of 100 feet per second, nd its velocity and height 5 seconds later. Velocity: feet per second, and height: feet Hint: It is possible to get a negative velocity. Negative velocity indicates the object is traveling downwards. The acceleration of an object moving along a coordinate line is given by (t) = [3: + 3]_5 in meters per second per second. It the velocity at t = D is 4 meters per second, nd the velocity 2 seconds later. 1.: : meters per second