• A student asked me what "rational coefficients" (used in 1c) meant. Part of my reply was the following:

  So "second order linear ordinary differential equation with rational
  coefficients" means that f should satisfy an equation of this type:
  
  A(z)f''(z)+B(z)f'(z)+C(z)f(z)=D(z)
  
  where the functions A(z), B(z), C(z), and D(z) are rational FUNCTIONS.
  
  If all of the four are supposed to be rational NUMBERS, then that's a
  constant coeff equation. If you substitute exp(rz) in the associated
  homogeneous equation, you will get a quadratic equation for r (the
  "characteristic equation" is what it is called, I think). Then the
  solutions will all be linear combinations of these exponentials (with
  something simple happening if the root is multiple). But I am fairly
  sure the dilogarithm is NOT a linear combination of exponentials (hey:
  the radius of convergence is finite!).
  

• The Midterm Exam Preparation problems should not be handed in. They are merely advisory for you to do with as you wish.

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