Reduction of Order (Introduction)

This ordinary differential equations video explains the reduction of order method for solving second-order differential equations. For this method, we must first know one solution from the fundamental solution set, in order to find the general solution, but this method allows us to solve both homogeneous and non-homogeneous 2nd-order equations. We use an example to explain how the method works, working through it fully and explaining the substitutions used as we go, reducing the equation to a first-order differential equation. We explain that reduction of order turns a homogeneous equation into a separable 1st-order equation, and a non-homogeneous equation into a linear equation. At the end, we provide an outline of the method of reduction of order.
0:00 Method Introduction
1:03 Explaining by example - Substitution
5:30 Reducing the Order
7:04 Solving the 1st-Order Equation
8:18 Substitution/Integration to solve
9:19 Reduction of Order Outline
Houston Math Prep Differential Equations Playlist: https://www.youtube.com/playlist?list=PLbYOkEbzW902GJZswbMnWHQaP4kKMS2TV
Houston Math Prep YouTube: https://www.youtube.com/user/HoustonMathPrep

Видео Reduction of Order (Introduction) канала Houston Math Prep