[Analysis] Add more notes

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

@@ -4,9 +4,9 @@
 \shortproposition Solution of $y' + ay = 0$ is of form $f(x) = C e^{-A(x)}$ with $A$ anti-derivative of $a$
 
 \rmvspace
-\shade{gray}{Imhomogeneous equation} 
+\shade{gray}{Imhomogeneous equation} $y' + ay = b$ with $b$ any function.
 \rmvspace
 \begin{enumerate}[noitemsep]
-    \item Find solution to $y_p = z(x) e^{-A(x)}$ with $z(x) = \int b(x) e^{A(x)} \dx x$ ($A(x)$ in exp here!),  
+    \item Compute $y_p = z(x) e^{-A(x)}$ with $z(x) = \int b(x) e^{A(x)} \dx x$ ($A(x)$ in exp here!),  
     \item Solve and the result is $y(x) = y_h + c \cdot y_p$. For initial value problem, determine coefficient $C$
 \end{enumerate}