Differential Equations

Separating variables: $\frac{dy}{y} = -2x dx \implies \ln(y) = -x^2 + C \implies y = A e^{-x^2}$. Since $y(0) = 1$, $A = 1$, so $y(x) = e^{-x^2}$. At $x=1$: $y(1) = e^{-1} = \frac{1}{2.71828} \approx 0.368$.