This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 334 Lecture #3 2.1: First Order Linear ODEs The first order ODEs dy dt = 1 5 y + 9 . 8 and ty = 4 t 2 2 y are examples of the general first order linear ODE dy dt + p ( t ) y = g ( t ) where p ( t ) and g ( t ) are functions continuous on a common open interval I . Method of Solution (Leibniz). The expression on the lefthand side of the differen tial equation, dy dt + p ( t ) y, is similar to the derivative of the product of y with a differentiable function, say, ( t ): d dt ( t ) y = ( t ) dy dt + ( t ) y. This suggests multiplying the ODE through by ( t ): ( t ) dy dt + ( t ) p ( t ) y = ( t ) g ( t ) . For the lefthand side of this to be [ ( t ) y ] requires that ( t ) satisfies the differential equation ( t ) p ( t ) = ( t ) . [To solve one differential equation we have to solve another differential equation! We will see this idea again and again.] Rewrite the ODE for with all the s on one side: ( t ) ( t ) = p (...
View
Full
Document
This note was uploaded on 03/08/2011 for the course MATH 334 taught by Professor Smith during the Spring '11 term at Vanderbilt.
 Spring '11
 Smith
 Math

Click to edit the document details