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b/semester3/analysis-ii/analysis-ii-cheat-sheet.tex index e14639e..6d99567 100644 --- a/semester3/analysis-ii/analysis-ii-cheat-sheet.tex +++ b/semester3/analysis-ii/analysis-ii-cheat-sheet.tex @@ -70,6 +70,7 @@ You could also print it as two A5 pages per A4 page and also print the \newsection \section{Differential Equations} \input{parts/diffeq/00_intro.tex} +\input{parts/diffeq/linear-ode/00_intro.tex} diff --git a/semester3/analysis-ii/parts/diffeq/linear-ode/00_intro.tex b/semester3/analysis-ii/parts/diffeq/linear-ode/00_intro.tex index 1b295b1..c1357f5 100644 --- a/semester3/analysis-ii/parts/diffeq/linear-ode/00_intro.tex +++ b/semester3/analysis-ii/parts/diffeq/linear-ode/00_intro.tex @@ -1,2 +1,5 @@ -\newsection +\newsectionNoPB \subsection{Linear Differential Equations} +\compactdef{Linear differential equation of order $k$} +$y^{(k)} + a_{k - 1}y^{(k - 1)} + \ldots + a_1 y' + a_0 y = b$, with $a_i$ and $b$ functions in $x$. +If $b(x) = 0 \smallhspace \forall x$, \bi{homogeneous}, else \bi{inhomogeneous}