documentclass{article}
usepackage{longtable,amsmath}
begin{document}
begin{longtable}{|p{0.05textwidth}|p{0.47textwidth}|p{0.47textwidth}|}
    hline
    &multicolumn{1}{|c|}{$Delta v=0$}&multicolumn{1}{c|}{$-Delta v=lambda v$}\
    hline
    2D & begin{multline*}C+Dln r \
    +left(A_nr^n+ frac{B_n}{r^n}right)(C_ncos ntheta+D_ncos ntheta) end{multline*} & begin{multline*} (A_nJ_n(sqrtlambda r)+B_nN_n(sqrtlambda r)) \
    times(C_ncos ntheta+D_nsin ntheta)end{multline*} \
    hline
    3D & begin{multline*} left(A_lr^l+frac{B_l}{r^{l+1}}right)P^m_l(costheta) e^{imphi}end{multline*} & begin{multline*}small frac{A_lJ_{l+1/2}(sqrtlambda r)+B_lN_{l+1/2}(sqrtlambda r)}{sqrt r} \
    times P^l_m(costheta)e^{imphi} end{multline*}
    hline
    end{longtable}
end{document}