Derive the differential equation(s) describing the given physical situation.
A rocket is shot vertically upward from the surface of the earth. After all its fuel has been expended, the mass of the rocket is a constant tn. Use New-ton's second law of motion and the fact that the force of gravity varies inversely as the square of the distance to find the differential equation for distance y from the earth's center to the rocket at time t after burnout. State appropriate conditions at t = 0 associated with this differential equation.
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