​​​​​​​Đáp án:

\( f'(x) + 2x f(x) = 2x e^{-x^2}  \Leftrightarrow e^{x^2} f'(x) + 2x e^{x^2} f(x) = 2x \).

(Gợi ý: \( \left((e^{x^2} f(x))' = 2x e^{x^2} f(x) + e^{x^2} f'(x) \right) \)):  

\( \Rightarrow \left(e^{x^2} f(x) \right)' = 2x \).

\( \Rightarrow e^{x^2} f(x) = x^2 + C \).

\( f(0) = 1  \Rightarrow \quad C = 1 \).

 \( f(x) = \frac{x^2 + 1}{e^{x^2}} \Rightarrow f(1)  = \frac{2}{e}\Rightarrow \boxed{C} \).