Linear differential equations are mathematical equations that involve an unknown function and its derivatives. They are called "linear" because the unknown function and its derivatives appear to the first power and are not multiplied together. These equations can be expressed in the standard form, where the highest derivative is isolated on one side of the equation. These equations are widely used in various fields, including physics, engineering, and economics, to model real-world phenomena. Solutions to linear differential equations can often be found using techniques such as integrating factors or characteristic equations, making them a fundamental topic in mathematics.