如何使表格中的某些单元格左对齐、在行之间添加空间以及使每个单元格垂直居中？

Question

我想制作一张表格。这是我的代码。

\documentclass{article}
\usepackage[left=2 cm,right=2cm,top=2cm,bottom=2cm]{geometry}
\usepackage{amsmath,array}
\renewcommand{\arraystretch}{1.2}
\newcolumntype{P}[1]{>{\centering\arraybackslash}p{#1}}
\begin{document}
    \begin{center}
        \begin{tabular}{|c|c|P{2cm}|P{1.5cm}|P{1.5cm}|P{1.5cm}|P{1.5cm}|}
            \hline
            &Differential Equations&Independent Variables&Dependent Variables&Linear/ Nonlinear& Order& Degree\\
            \hline
            a.&$x^2\dfrac{d^2y}{dx^2}-6y\dfrac{dy}{dx}=0$&$x$&$y$&linear&$2$&$1$\\
            \hline
            b.&$\dfrac{d^2Q}{dt^2}-6\dfrac{dQ}{dt}+10Q=4$&$t$&$Q$&linear&$2$&$1$\\
            \hline
            c.&$2y\left(\dfrac{d^3y}{dx^3}\right)^2+5\dfrac{dy}{dx}+2xy=\cos x$&$x$&$y$&non linear&$3$&$2$\\
            \hline
            d.&$\dfrac{\partial u}{\partial x}+\dfrac{\partial u}{\partial t}+xt=0$&$x, t$&$u$&linear&$1$&$1$\\
            \hline
            e.&$1+\left(\dfrac{dy}{dx}\right)^2=3\dfrac{d^2y}{dx^2}$&$x$&$y$&non linear&$2$&$1$\\
            \hline
        \end{tabular}
    \end{center}
\end{document}

现在我想将表格修改成如下图所示：

（1）我希望第二列、第二行直到第六行左对齐。

（2）我希望所有单元格都垂直居中。

（3）我想为每一行添加额外的空间。

谁能帮我写这个表格？

Answer 1

像这样：

（红线表示文字边框）

借助makecell软件包：

\documentclass{article}
\usepackage[margin=2cm]{geometry}
%---------------- show page layout. don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%---------------------------------------------------------------%

\usepackage{amsmath}
\usepackage{makecell}
\newcolumntype{P}[1]{>{\centering\arraybackslash}p{#1}}

\begin{document}
    \begin{center}
    \setcellgapes{5pt}
    \makegapedcells
\begin{tabular}{|c| l | *{5}{c|} }
    \Xhline{1.2pt}
    & \makecell{Differential Equations}
        & \makecell{Independent\\ Variables}
            & \makecell{Dependent\\ Variables}
                & \makecell{Linear/\\ Nonlinear}
                    & Order
                        & Degree                \\
    \Xhline{0.8pt}
a.  & $x^2\dfrac{d^2y}{dx^2}-6y\dfrac{dy}{dx}=0$
        & $x$ & $y$ & linear & $2$ & $1$        \\
    \hline
b.  & $\dfrac{d^2Q}{dt^2}-6\dfrac{dQ}{dt}+10Q=4$
        & $t$ & $Q$ & linear & $2$ & $1$        \\
            \hline
c.  & $2y\left(\dfrac{d^3y}{dx^3}\right)^2+5\dfrac{dy}{dx}+2xy=\cos x$
        & $x$ & $y$ & non linear & $3$ & $2$    \\
    \hline
d.  & $\dfrac{\partial u}{\partial x}+\dfrac{\partial u}{\partial t}+xt=0$
            & $x, t$ & $u$ & linear & $1$ & $1$ \\
    \hline
e.  & $1+\left(\dfrac{dy}{dx}\right)^2=3\dfrac{d^2y}{dx^2}$
        & $x$ & $y$ & non linear & $2$ & $1$    \\
    \Xhline{1.2pt}
\end{tabular}
    \end{center}
\end{document}