2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230857DNA's shape mostly lies on its total energy $F$. Its corresponding equilibrium shape equations can be got by classical variation method: letting the first energy variation $δ^{(1)}F=0$. Here we not only provide the first variation $δ^{(1)}F$ but also give the second variation $δ^{(2)}F$ in planar case. Moreover, the general shape equations of DNA are obtained and a mistake in [Zhang, \emph{et al}. {\it Phys. Rev. E} {\bf 70} 051902 (2004)] is pointed out.9 pages, 1 figure,. Accepted by International Journal of Modern Physics BSoft Condensed MatterOther Condensed Mattertext