Let b be a nonzero real number. Suppose $f: \mathbb{R} \rightarrow \mathbb{R}$ is a differentiable function such that $(0)=1$. If the derivative $f^{\prime}$ of $f$ satisfies the equation $\mathrm{f}^{\prime}(\mathrm{x})=\frac{\mathrm{f}(\mathrm{x})}{\mathrm{b}^2+\mathrm{x}^2}$ for all $x \in \mathbb{R}$, then which of the following statements is/are TRUE?