• 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.