Integrating factor for non-exact differential equations - Copy (2)

Integrating factor for non-exact differential equations - Copy (2)

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
A. Alaca MATH 1005 Winter 2010 8 Integrating factor for non-exact differential equations It is sometimes possible to convert a non-exact DE into an exact DE by multiplying it an integrating factor I ( x, y ): P ( x, y )+ Q ( x, y ) y ± =0 ( * ) (non-exact.) I ( x, y ) P ( x, y I ( x, y ) Q ( x, y ) y ± = 0 (exact) ∂y ( IP )= ∂x ( IQ )or I y P + y = I x Q + x or PI y - QI x = I ( Q x - P y )( ** ) In general, to solve ( ** ) is harder than to solve ( * ). But if I = I ( x ) (or I = I ( y )), then we can solve ( ** ). If I = I ( x ), then I y = 0 and ( ** ) becomes - QI x =( Q x - P y ) I = dI dx = P y - Q x Q I = dI I = P y - Q x Q dx. After we integrate and rise both side to e , we obtain | I | = e ± 1 Q ( P y - Q x ) dx .
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/08/2010 for the course MATH 1005 taught by Professor Any during the Winter '07 term at Carleton CA.

Ask a homework question - tutors are online