Let $$y = y_1(x)$$ and $$y = y_2(x)$$ be the solution curves the differential equation $$\frac{dy}{dx} = y + 7$$ with initial conditions $$y_1(0) = 0$$ and $$y_2(0) = 1$$ respectively. Then the curves $$y = y_1(x)$$ and $$y = y_2(x)$$ intersect at

Given: $$\frac{dy}{dx} = y + 7$$, $$y_1(0) = 0$$, $$y_2(0) = 1$$.

Solve the ODE: $$\frac{dy}{y+7} = dx$$, so $$\ln|y+7| = x + C$$, giving $$y + 7 = Ae^x$$.

$$y_1$$: $$0 + 7 = A$$, so $$y_1 = 7e^x - 7$$.

$$y_2$$: $$1 + 7 = A$$, so $$y_2 = 8e^x - 7$$.

For intersection: $$7e^x - 7 = 8e^x - 7$$, i.e., $$7e^x = 8e^x$$, which gives $$e^x = 0$$. No solution.

The curves never intersect.

The correct answer is Option A: no point.