$$y''-xy=0$$
$$x^2y''+xy'+(x^2-n^2)y=0 $$
$$(1-x^2)y''-2xy'+n(n+1)y=0$$
$$xy''+(k+1-x)y'+(n-k)y=0$$
$$y''-2xy'+2ny=0$$
$$x(1-x)y''+(\gamma-(\alpha+\beta+1)x)y'-\alpha\beta y=0$$
$$y''+(\lambda-x^2)y=0$$