[Analysis] Start constant coefficients section

semester3/analysis-ii/parts/diffeq/linear-ode/01_order-one.tex

@@ -5,3 +5,5 @@
 \bi{(3)} If initial conditions, find equations $\in \mathcal{S}_b$ which fulfill conditions using SLE (as always)
 
 \shortproposition Solution of $y' + ay = 0$ is of form $f(x) = z e^{-A(x)}$ with $A$ anti-derivative of $a$
+
+\TODO Improve procedure with notes from session \& SPAM

semester3/analysis-ii/parts/diffeq/linear-ode/02_constant-coefficient.tex

@@ -1,3 +1,6 @@
 \newsectionNoPB
 \subsection{Linear differential equations with constant coefficients}
-The coefficients $a_i$ are constant functions of form $a_i(x) = k$ with $k$ constant.
+The coefficients $a_i$ are constant functions of form $a_i(x) = k$ with $k$ constant, where $b(x)$ can be any function.\\
+%
+\shade{gray}{Solving:} \bi{(1)} Find \textit{characteristic polynomial} (of form $\lambda^k + a_{k - 1} \lambda^{k - 1} + \ldots + a_1 \lambda + a_0$ for order $k$ lin. ODE with coefficients $a_i$).
+Find the roots of polynomial.