1. **State the problem:** Find the general solution of the differential equation $$\frac{dy}{dx} = xy$$ for $$y > 0$$. 2. **Identify the type of differential equation:** This is a first-order separable differential equation because the right side can be written as a product of a function of $$x$$ and a function of $$y$$. 3. **Separate variables:** Rewrite the equation as $$\frac{dy}{y} = x\,dx$$. 4. **Integrate both sides:** $$\int \frac{1}{y} dy = \int x \, dx$$ which gives $$\ln|y| = \frac{x^2}{2} + C$$ where $$C$$ is the constant of integration. 5. **Solve for $$y$$:** Since $$y > 0$$, we can drop the absolute value and exponentiate both sides: $$y = e^{\frac{x^2}{2} + C} = e^C e^{\frac{x^2}{2}}$$. 6. **Simplify the constant:** Let $$A = e^C > 0$$, so the general solution is $$y = A e^{\frac{x^2}{2}}$$. **Final answer:** $$\boxed{y = A e^{\frac{x^2}{2}} \text{ where } A > 0}$$.