diff --git a/semester3/analysis-ii/cheat-sheet-rb/main.pdf b/semester3/analysis-ii/cheat-sheet-rb/main.pdf
index 5287e4f..53f35c4 100644
Binary files a/semester3/analysis-ii/cheat-sheet-rb/main.pdf and b/semester3/analysis-ii/cheat-sheet-rb/main.pdf differ
diff --git a/semester3/analysis-ii/cheat-sheet-rb/parts/03_diffeq_sol.tex b/semester3/analysis-ii/cheat-sheet-rb/parts/03_diffeq_sol.tex
index b66a881..1f932d0 100644
--- a/semester3/analysis-ii/cheat-sheet-rb/parts/03_diffeq_sol.tex
+++ b/semester3/analysis-ii/cheat-sheet-rb/parts/03_diffeq_sol.tex
@@ -70,7 +70,7 @@ $$
 \remark If $\alpha_j = \beta + \gamma i \in \C$ is a root, $\bar{\alpha_j} = \beta - \gamma i$ is too.\\
 To get a real-valued solution, apply:
 $$
-e^{\alpha_j x} = e^{\beta x}\left( \cos(\gamma x) + i \sin(\gamma x) \right)
+e^{\alpha_j x} + e^{\alpha_i x} = e^{\beta x}\left( \cos(\gamma x) + \sin(\gamma x) \right)
 $$
 
 \begin{subbox}{Explicit Homogeneous Solution}