L05 - Integrating Factors Suppose the FOODE M (x, y ) dx +...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Integrating Factors Suppose the FOODE M ( x,y ) dx + N ( x,y ) dy = 0 is not exact. The previous example leads to the question: Can we multiply it by some function μ = μ ( x,y ) , to be called an Integrating factor , so that ( μ ( x,y ) M ( x,y ) ) dx + ( μ ( x,y ) N ( x,y ) ) dy = 0 is exact? We need μ y M + μM y = μ x N + μN x . ( IF )
Background image of page 1

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

View Full DocumentRight Arrow Icon
Integrating Factors Suppose the FOODE M ( x,y ) dx + N ( x,y ) dy = 0 is not exact. The previous example leads to the question: Can we multiply it by some function μ = μ ( x,y ) , to be called an Integrating factor , so that ( μ ( x,y ) M ( x,y ) ) dx + ( μ ( x,y ) N ( x,y ) ) dy = 0 is exact? We need μ y M + μM y = μ x N + μN x . ( IF ) This is a PDE for μ , much too hard. Sometimes it it possible to find an inte-
Background image of page 2
grating factor μ that depends only on x : μ = μ ( x ) . Then ( IF ) reads μ 0 ( x ) = μ ( x ) M y ( x,y ) - N x ( x,y ) N ( x,y ) . ( IF x ) If the quotient on the right does not de- pend on y , we have our μ = μ ( x )
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/29/2009 for the course M 427K taught by Professor Fonken during the Fall '08 term at University of Texas at Austin.

Page1 / 8

L05 - Integrating Factors Suppose the FOODE M (x, y ) dx +...

This preview shows document pages 1 - 4. Sign up to view the full document.

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