Consider the initial value problem
$$
y^{\prime \prime}+2 a y^{\prime}+\left(a^2+1\right) y=0, \quad y(0)=1, \quad y^{\prime}(0)=0 .
$$
For $a=1$ find the smallest $T$ such that $|y(t)|<0.1$ for $t>T$.
1.8763