Linear Differential Equations

Linear differential equations are equations that involve a function and its derivatives, with the key property that the function and its derivatives appear in a linear form—meaning no products or powers. They describe how a quantity changes over time or space, such as population growth or heat flow. These equations are called “linear” because their solutions can often be combined straightforwardly, allowing for predictable analysis and solutions. They are fundamental tools in science and engineering, providing a way to model and understand systems where change is proportional to the current state or its rate of change.