{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

L23 - Fall 2003 Math 308/501–502 2 First-Order...

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 Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Fall 2003 Math 308/501–502 2 First-Order Differential Equations 2.3 Linear Equations Wed, 10/Sep c 2003, Art Belmonte Summary We saw in §1 . 1 that a first-order linear differential equation has the form a 1 ( x ) dy dx + a ( x ) y = b ( x ) . The coefficients a , a 1 , b are constants or functions of the independent variable x alone; they do not depend on the dependent variable y . Moreover, note that both y and its derivative y occur to the first power only. The equation is homogeneous if b ( x ) = 0 and nonhomogeneous if b ( x ) 6= 0. Conventional procedure (CP) 1. You MUST put the DE in standard linear form ( SLF ): y + P ( x ) y = Q ( x ) 2. Construct an integrating factor μ( x ) = exp ( R P ( x ) dx ) . Note that any antiderivative R p ( x ) dx will do. So take the constant of integration to be zero. 3. Multiply the SLF by the integrating factor μ to obtain μ y + μ Py = μ Q . Notice by design that (μ y ) = μ y + μ y = μ y + μ Py (via the Chain Rule). Putting these two together gives (μ( x ) y ( x )) = μ( x ) Q ( x ) which is separable. That is, it’s of the form d w/ dx = g ( x ) and we may use §2 . 2 techniques!...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

L23 - Fall 2003 Math 308/501–502 2 First-Order...

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

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