### Classification of initial data for the Riccati equation

We consider a Cauchy problem $${y}^{\prime}\left(x\right)+{y}^{2}\left(x\right)=q\left(x\right),{\left.y\left(x\right)\right|}_{x={x}_{0}}={y}_{0}$$ where ${x}_{0}$ , ${y}_{0}\in \mathbb{R}$ and $q\left(x\right)\in {L}_{1}^{\text{loc}}\left(R\right)$ is a non-negative function satisfying the condition: $${\int}_{-\mathrm{\infty}}^{x}q\left(t\right)dt>0,{\int}_{x}^{\mathrm{\infty}}q\left(t\right)dt>0\text{for}x\in \mathbb{R}.$$ We obtain the conditions under which $y\left(x\right)$ can be continued to all of $\mathbb{R}$. This depends on ${x}_{0}$ , ${y}_{0}$ and the properties of $q\left(x\right)$.