Let $\mathrm{y}={\mathrm{y}}_1\left(\mathrm{x}\right)\text{and }\mathrm{y}={\mathrm{y}}_2\left(\mathrm{x}\right)$ be the solution curves of the differential equation $\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{y}+7$ with initial conditions ${\mathrm{y}}_1\left(0\right)=0$ and ${\mathrm{y}}_2\left(0\right)=1$ respectively.  Then the curves $\mathrm{y}={\mathrm{y}}_1\left(\mathrm{x}\right)$ and $\mathrm{y}={\mathrm{y}}_2\left(\mathrm{x}\right)$ intersect at

$$\begin{gathered} \frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{y}+7\Rightarrow \frac{\mathrm{dy}}{\mathrm{y}+7}=\mathrm{dx}\Rightarrow \ln |\mathrm{y}+7|=\mathrm{x}+\mathrm{c} \\ {\mathrm{y}}_1\left(0\right)=0\Rightarrow \ln 7=\mathrm{c} \end{gathered}$$
${\mathrm{y}}_2\left(0\right)=1\Rightarrow \ln 8=\mathrm{c}$
The curves are $\ln (\mathrm{y}+7)=\mathrm{x}+\ln 7 \mathrm{and} \ln (\mathrm{y}+7)=\mathrm{x}+\ln 8$
i.e., $\mathrm{y}=7{\mathrm{e}}^{\mathrm{x}}-7..........\left(1\right)$  and $\mathrm{y}=8{\mathrm{e}}^{\mathrm{x}}-7.............\left(2\right)$
(1) and (2) don’t  intersect