how to have more control on the anchor location of a node other than defaults?

Question

A tikz node has anchor points south, north etc.. also south west and south east etc...

But in this diagram below, I'd like to draw a line from a node starting not at exactly south west but half way between south west and south. i.e. shifted more to to the right from the south west corner so it looks better.

How does one create a new anchor location in general to use to draw lines from other than those buildin?

An example will make this clear. This MWE

\documentclass{article}    
\usepackage{tikz}
\usetikzlibrary{shapes,arrows}
\usetikzlibrary{positioning}
\begin{document}
\pagestyle{empty}
    
\tikzstyle{block} = [rectangle, draw, fill=blue!20, 
    text width=5em, text centered, rounded corners, minimum height=4em]
\tikzstyle{line} = [draw, -latex']
    
\begin{tikzpicture}
    % Place nodes
    \node [block] (init) {differential equation};
    %
    \node [block, below right=1cm and -1.5cm  of init] (secondOrder) {second order};
    %
       \node [block, below=1cm of secondOrder] (linearSecondOrder) {linear};
       \node [block, right=1cm of linearSecondOrder] (nonlinearSecondOrder) {non-linear};
    %
    \node [block, below left=1cm and 1cm  of init] (firstOrder) {first order};
    %
       \node [block, below=1cm of firstOrder] (firstOrderDegree1) {degree 1};
           %
           \node [block, below right=.5cm and -1.2cm of firstOrderDegree1] (linearFirstOrder) {linear};
           \node [block, below=.5cm of linearFirstOrder]  (separable) {separable};
           \node [block, below=.5cm of separable]   (bernoulli) {Bernoulli};
       %
       \node [block, left=1cm of firstOrderDegree1] (firstOrderDegreeHigher) {higher degree};
    %
    \node [block,   below right=1cm and 4.5cm of init] (higherOrder) {higher order};
     

    \path [line] (init) -- (firstOrder);
    \path [line] (init) -- (secondOrder);
    \path [line] (init) -- (higherOrder);
    %
    \path [line] (secondOrder) -- (linearSecondOrder);
    \path [line] (secondOrder) -- (nonlinearSecondOrder);
    %
    \path [line] (firstOrder) -- (firstOrderDegree1);
    \path [line] (firstOrder) -- (firstOrderDegreeHigher);
    %
    \path [line] (firstOrderDegree1.south west) -- (linearFirstOrder.west);
    \path [line] (firstOrderDegree1.south west) -- (separable.west);
    \path [line] (firstOrderDegree1.south west) -- (bernoulli.west);    
\end{tikzpicture}    
\end{document}

Generates this

Actually what I'd like to do is the following, but I think this is harder so I am try first to see if I can change the anchor location first:

The above is better, but I do not know how do the above, since I do not know the locations to draw the lines from/to. So I'll settle for the first choice for now if possible.

Answer 1

Here is an option using forest.

\documentclass{article}

\usepackage[edges]{forest}

\begin{document}

\begin{forest}
for tree={
    draw, rounded corners, fill=blue!20,
    minimum height=1.5cm, minimum width=2cm,
    align=center, base=b,
    s sep=1cm, l sep=.5cm,
    if level<=2{edge=-latex}{edge=red},
}
[differential\\equation
    [first order, calign=last
        [higher\\degree][degree 1, for tree={grow'=0, folder}, s sep=.5cm, before computing xy={l-=.845cm}
            [linear][separable][Bernoulli]
        ]
    ]
    [second order, calign=first
        [linear][nonlinear]
    ]
    [higher order, fit=band]
]
\end{forest}

\end{document}