If \(y=A(x)\cdot e^{-x^2\) is a solution of the differential equation}
\[
\frac{dy}{dx}+2xy=2e^{-x^2}
\]
with \(y(0)=-3\), then the value of \(A(1)\) is ____.
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For equations of the form
\[
\frac{dy}{dx}+P(x)y=Q(x),
\]
use
\[
\boxed{
\text{I.F.}=e^{\int P(x)\,dx}.
}
\]