differential equations integrating factors

Differential equations integrating factors are equations that involve derivatives of unknown functions, along with the unknown functions themselves. In order to solve these equations, you need to use an integrating factor, which is a multiplier that allows you to simplify the equation and solve for the unknown function. For example, if you had the differential equation 4y’ + 6y = 4x, you would use an integrating factor of 2 to solve it. After multiplying both sides of the equation by 2, you would get 8y’ + 12y = 8x, which is much easier to solve. An analogy to explain integrating factors is that of a particle moving along a curved path. To find the particle’s position at any given point in time, you need to use an integrating factor to help you solve for it. A fun fact about integrating factors is that they were first used by Leonhard Euler in the 18th century, and he used them to solve equations related to planetary motion.