Exam 2 Grading method

[goodwine]

• Problem 1.
  Part a)
  - 5 pts for correct assumption of the form of x and calculation of x_dot
  - 5 pts for work including substitution into given equation and reducing to single variable
  - 5 pts for proper recursive form
  
  Part b)
  - 5 pts for proper exponential solution to ODE
  - 5 pts for all work leading to Taylor series expansion
  
  In most cases, 1 or 2 pts was the maximum deducted if work was shown, and in one or two instances, 3 pts was deducted when I felt there was a more significant lack of understanding displayed in the work.
  
  In rare occasions, some parts of the problems contained no work, these parts received 0 points.
• Problem 2.
  +5 for 3 initial assumptions
  +5 ended up with a2 = 0 (using a correct method)
  +10 for the recursion reconstruction equation, with steps shown (minus 1-2 pts for slight math errors)
  +5 for all 6 correct terms
• Problem 3.
  (5) Singular point
  (5) Regular singular point (1pt for yes; 4 pts for why)
  (5) Correct series representation of x
  (10) Calculations
• Problem 4.
  (5) Series representation of x
  (5) Collect of t^n on LHS
  (15) Calculation of a_0, a_1, a_2, a_3, a_{n+2}
  Notes:
  (10) Correct representation of a_{n+2}
  (5) Other calculations and final answer