> There might even be some automated algorithm to do all the steps above
> and spit out the final coefficients "a", "b" and "x",
> but for now I am happy to do it explicitly.
Maybe like this?
>>> eq
2*Z*F(r) - 2*l*lam*F(r) + 2*l*Derivative(F(r), r) -
2*lam*r*Derivative(F(r), r) - 2*lam*F(r) + r*Derivative(F(r), r, r) +
2*Derivative(F(r), r)
>>> f,df,d2f
(F(r), Derivative(F(r), r), Derivative(F(r), r, r))
>>> a,b,x
(a, b, x)
>>> solve([eq.coeff(w) - z for w, z in [ (d2f, x), (df, b-x), (f, -a) ]], a,b,x)
{x: r, b: 2*l - 2*lam*r + r + 2, a: -2*Z + 2*l*lam + 2*lam}
/c
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