Mathematica：
Consider homogeneous linear differential equation of the 2d order
f(x) y″+ g(x) y′ + h(x) y = 0
Switch it to the so-called "normal" form of a differential equation by changing variables in order to get rid of the 1st derivative:
u(x) = y(x) exp {(1/2)∫(g/f)dx}
will give
u″ + I(x)u = 0
with
I = h/f - (1/4)(g/f)^2 - 1/2 (g/f)′
Homework: check this using Mathematica. Write a pure function which calculates I(x) for any f, g, h.
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