<|system|>
Consider the initial value problem
$$
y^{\prime}+\frac{2}{3} y=1-\frac{1}{2} t, \quad y(0)=y_0 .
$$
Find the value of $y_0$ for which the solution touches, but does not cross, the $t$-axis.</s>.
<|user|>
Can you answer based on context?
<|assistant|>
−1.642876