1. **Problem Statement:** Solve the differential equation using the method of separable variables. 2. **General Approach:** A separable differential equation can be written as $$\frac{dy}{dx} = g(x)h(y)$$ which can be rearranged to $$\frac{1}{h(y)} dy = g(x) dx$$. 3. **Step-by-step Solution:** - Separate variables: move all terms involving $y$ to one side and all terms involving $x$ to the other. - Integrate both sides: $$\int \frac{1}{h(y)} dy = \int g(x) dx + C$$ where $C$ is the constant of integration. - Solve the resulting equation for $y$ if possible. 4. **Important Notes:** - Always check the domain of the solution. - The constant $C$ represents the family of solutions. This method transforms the differential equation into integrals that can be evaluated to find the implicit or explicit solution for $y$ in terms of $x$.