diff --git a/.translate/state/samuelson.md.yml b/.translate/state/samuelson.md.yml
index 18dbb6c5..f01fd9c6 100644
--- a/.translate/state/samuelson.md.yml
+++ b/.translate/state/samuelson.md.yml
@@ -1,6 +1,6 @@
-source-sha: e49ee52fb9a5209e678973ed8226c7ea0b4fc88e
-synced-at: "2026-07-31"
+source-sha: 285b3fe8d1a5df2402ecd2b8e0e8cf72d1932cf3
+synced-at: "2026-09-26"
 model: claude-sonnet-5
 mode: UPDATE
 section-count: 9
-tool-version: 0.24.0
+tool-version: 0.29.3
diff --git a/lectures/samuelson.md b/lectures/samuelson.md
index 5a16006e..1ad69310 100644
--- a/lectures/samuelson.md
+++ b/lectures/samuelson.md
@@ -657,17 +657,17 @@ def y_nonstochastic(y_0=100, y_1=80, α=0.92, β=0.5, γ=10, n=80):
     discriminant = ρ1**2 + 4 * ρ2
 
     if discriminant == 0:
-        roots.append(-ρ1 / 2)
+        roots.append(ρ1 / 2)
         print("单个实根：")
         print("".join(f"{r:.2f}" for r in roots))
     elif discriminant > 0:
-        roots.append((-ρ1 + sqrt(discriminant).real) / 2)
-        roots.append((-ρ1 - sqrt(discriminant).real) / 2)
+        roots.append((ρ1 + sqrt(discriminant).real) / 2)
+        roots.append((ρ1 - sqrt(discriminant).real) / 2)
         print("两个实根：")
         print(" ".join(f"{r:.2f}" for r in roots))
     else:
-        roots.append((-ρ1 + sqrt(discriminant)) / 2)
-        roots.append((-ρ1 - sqrt(discriminant)) / 2)
+        roots.append((ρ1 + sqrt(discriminant)) / 2)
+        roots.append((ρ1 - sqrt(discriminant)) / 2)
         print("两个复根：")
         print(" ".join(f"{r.real:.2f}{r.imag:+.2f}j" for r in roots))
 
@@ -926,7 +926,7 @@ plot_y(y_stochastic_g(g=500, g_t=50, duration="one-off"))
 
 ```{code-cell} ipython3
 class Samuelson:
-    """
+    r"""
     这个类代表萨缪尔森模型，也称为多重加速器模型。
     该模型将凯恩斯乘数与投资加速器理论相结合。
 
@@ -934,7 +934,7 @@ class Samuelson:
 
     .. math::
 
-        Y_t = \alpha (1 + \beta) Y_{t-1} - \alpha \beta Y_{t-2}
+        Y_t = (\alpha + \beta) Y_{t-1} - \beta Y_{t-2} + (\gamma + G_t) + \sigma \epsilon_t
 
     参数
     ----------