A 30 year old woman is admitted to the hospital unable to be…

A 30 year old woman is admitted to the hospital unable to bear weight on both legs.  Imaging shows a vertebrae that has been reduced from 1.5 inches in height to 0.5 inches.  The swelling and excess bone material has put pressure on the woman’s spinal cord resulting in partial paralysis.  What type of fracture has she been diagnosed with?

(3 points for the correct answer; 1 bonus point if you have…

(3 points for the correct answer; 1 bonus point if you have correctly answered questions 1 through 3.) Determine the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. (Do not attempt to find the solution.)