# How to make the table is left aligned for some cells, adding space between row, and vertically centered for every cells?

I want make a table. This is my code.

\documentclass{article}
\usepackage[left=2 cm,right=2cm,top=2cm,bottom=2cm]{geometry}
\usepackage{amsmath,array}
\renewcommand{\arraystretch}{1.2}
\newcolumntype{P}{>{\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}


Now I want to modify the table as this picture: (1) I want for second column, for second until sixth row is left aligned.

(2) I want for all cell is vertically centered.

(3) I want to add extra space for every row.

Anyone can help me how to write this table?

Like this: (red lines shows text borders)

With help of makecell packages:

\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}{>{\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}