Mathematics - Indefinite Integration Question with Solution | TestHub

Let $f(\mathrm{x})$ be a differentiable function satisfying the equation $\frac{f^{\prime }(\mathrm{x})}{2}=\frac{\mathrm{x}}{{\mathrm{e}}^{f(\mathrm{x})}}\forall \mathrm{x}\in \mathrm{R}$. If $f^{\prime }(1)=1$, then the number of solution(s) of the equation $f^{\prime }(\mathrm{x})=f(\mathrm{x})$ is