1. **State the problem:** We need to find the general solution of the differential equation $$\frac{dy}{dx} = \frac{y}{x}$$. 2. **Rewrite the equation:** The equation can be written as $$\frac{dy}{dx} = \frac{y}{x}$$. 3. **Separate variables:** We separate variables to isolate $y$ and $x$ on different sides: $$\frac{dy}{y} = \frac{dx}{x}$$. 4. **Integrate both sides:** Integrate both sides with respect to their variables: $$\int \frac{1}{y} dy = \int \frac{1}{x} dx$$. 5. **Perform the integration:** $$\ln|y| = \ln|x| + C$$, where $C$ is the constant of integration. 6. **Solve for $y$:** Exponentiate both sides to solve for $y$: $$|y| = e^{\ln|x| + C} = e^{\ln|x|} \cdot e^C = |x| \cdot e^C$$. 7. **Simplify the constant:** Let $A = \pm e^C$ (absorbing the absolute value and sign), so $$y = A x$$. **Final answer:** The general solution to the differential equation is $$y = A x$$ where $A$ is an arbitrary constant.