In the world of mathematics, a differential equation is an equation that relates a function to its derivatives. These equations are crucial because they describe various physical phenomena, such as heat, sound, electricity, and motion. For example, the differential equation: links the function to its first and second derivatives. When solving differential equations, the goal is typically to find the function that satisfies the equation given certain conditions. This function is a solution to the differential equation.
- The differential equation can be either ordinary (ODE) or partial (PDE), depending on whether it involves ordinary derivatives or partial derivatives.
- Order and degree are important concepts in differential equations, where the "order" refers to the highest derivative present, and "degree" when applicable, refers to the power of the highest derivative.
In this exercise, we are dealing with an ordinary differential equation (ODE) of the second order.