# L05 - Integrating Factors Suppose the FOODE M x,y dx N x,y...

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

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 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 ) 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- grating factor μ that depends only on x : μ = μ ( x ) . Then ( IF ) reads μ ( 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 ) : it is the...
View Full Document

{[ snackBarMessage ]}

### Page1 / 8

L05 - Integrating Factors Suppose the FOODE M x,y dx N x,y...

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

View Full Document
Ask a homework question - tutors are online