Somewhat off-topic, but if you are writing a DE final examination this
weekend, you may
enjoy the short Maxima program:
gen_de(sol, dvar, ivar, const) := block([de ],
sol : [sol, diff(sol,ivar),diff(sol,ivar,2)],
de : eliminate(sol, const),
de : solve(de, diff(dvar,ivar,2)),
ratsimp(first(de))
)$
(c1) depends(y,x)$
(c2) gen_de(y=k1*(x+x^3)*x^(-3/2) + k2 * x*x^(-3/2),y,x,[k1, k2]);
(c3) 'diff(y,x,2) = 3*y/(4*x^2)
(c4) latex(%);
$$ \frac {d^{2} y}{d x^{2}}=\frac {3\,y}{4\,x^{2}} $$
Wunderbar. To me Maxima is fun, but it also about doing real work quickly and accurately.
For all the folks that have made this possible, I thank you.
--blw