Variation - Variation of Parameters Recall that our last...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Variation of Parameters Recall that our last theorem states that the nonhomogeneous equation y 00 + p ( x ) y + q ( x ) y = g ( x ) has the general solution y ( x ) = ( x ) + c 1 y 1 ( x ) + c 2 y 2 ( x ) where ( x ) is a particular solution to the nonhomogeneous equation and c 1 y 1 ( x ) + c 2 y 2 ( x ) is the general solution to the nonhomogeneous equation. As a result, we would like a way to generate a particular solution ( x ) , assuming we have already solved the somewhat easier homogeneous equation. That is, given a fundamental set of solutions y 1 and y 2 to the homogeneous equation, can we come up a particular solution to the nonhomogeneous equation. The answer is yes, and the following method illustrates how this is possible. Variation of Parameters We will follow a strategy similar to the one we used in the Reduction of Order method, in the sense that we will try a solution of the form ( x ) = u 1 ( x ) y 1 ( x ) + u 2 ( x ) y 2 ( x ) and see if we can find conditions on the functions...
View Full Document

Page1 / 3

Variation - Variation of Parameters Recall that our last...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online