Unformatted text preview: y + a y + by = f x ( ) where a and b are constants. When f ( x ) = 0, the equation is called a homogeneous equation ; otherwise it is called an inhomogeneous equation . Any solution of this equation can be rewritten as a linear superposition of any two linearly independent solutions of this equation. Any solution will have two parameters that need to be adjusted to match the initial conditions. We start by first looking at the homogeneous equation. Consider the following solution of this equation: y x ( ) = e rx If we substitute this solution into the homogeneous equation we get r 2 + ar + b = In general there are two possible values of r :...
View Full Document
This note was uploaded on 01/08/2012 for the course PHY 235 taught by Professor Morgan during the Spring '09 term at SUNY Stony Brook.
- Spring '09