1. The problem is to solve the differential equation $$\frac{dy}{dx} = e^x y^2$$. 2. This is a separable differential equation, which means we can write it as $$\frac{dy}{y^2} = e^x dx$$. 3. Integrate both sides: $$\int y^{-2} dy = \int e^x dx$$ 4. The integral of $$y^{-2}$$ is $$-y^{-1}$$ and the integral of $$e^x$$ is $$e^x$$, so: $$-\frac{1}{y} = e^x + C$$ where $$C$$ is the constant of integration. 5. Solve for $$y$$: $$y = -\frac{1}{e^x + C}$$. 6. This is the general solution to the differential equation. Final answer: $$y = -\frac{1}{e^x + C}$$