Final answer:
In mathematics, the reduction of order is a strategy to find a second solution to a second-order differential equation, assuming that one solution is already known, by transforming it into a first-order equation.
Step-by-step explanation:
The question pertains to the method of reduction of order, which is a technique used in solving linear second-order differential equations when one solution is known. The goal here is to find a second independent solution using the known solution, typically by introducing a variable that transforms the second-order equation into a first-order equation. The first step involves assuming the second solution to be a product of the known solution and an unknown function. Then, you proceed by substituting this assumed solution and its derivatives into the original differential equation.
Simplifying the resulting equation often leads to a first-order equation that can be integrated to find the unknown function. This process is applied to equations like the rate constant and initial concentration relationship in second-order reactions within a chemistry context or to mechanical systems like a mass on a string or RC circuits in physics.