A separable differential equation is a first-order differential equation that can be rewritten so that all terms involving the dependent variable, typically \(y\) , are on one side of the equation and all terms involving the independent variable, \(x\) , are on the other. The discussion begins with the mathematical criteria for separability and the systematic multi-step process of rearrangement, integration, and constant aggregation required to find a general solution. Through a series of comprehensive examples, the text examines various solution types, including explicit and implicit functions, while highlighting the importance of identifying singular solutions where algebraic divisions might otherwise be undefined. The chapter further addresses initial value problems, demonstrating how specific conditions are used to determine unique constants. Advanced techniques are also introduced, such as using substitution to transform non-separable equations—specifically those involving linear combinations of variables—into a separable form. Finally, the integration of MATLAB is showcased, providing readers with the computational tools necessary to solve, verify, and visualize complex differential and integral equations efficiently.