notes 1-3 - y ( n ) = f ( t,y,y ,y 00 ,...,y ( n-1) ). A...

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

View Full Document Right Arrow Icon
SECTION 1.3 CLASSIFICATION OF DIFFERENTIAL EQUATIONS Ordinary versus partial, depending on the number of independent variables Order: the order of the highest derivative that appears Linear versus nonlinear, depending on whether anything is done to the unknown func- tion and its derivatives other than multiplying them by a function of the independent variable Suppose we have an ordinary differential equation (ODE) of order n . We always assume we can solve the ODE for the highest derivative, so we can write the equation as
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y ( n ) = f ( t,y,y ,y 00 ,...,y ( n-1) ). A solution of this ODE on the interval < t < is a function ( t ) such that all the derivatives of ( t ) up to order n exist everywhere in the interval and satisfy ( n ) ( t ) = f ( t, ( t ) , ( t ) ,..., ( n-1) ( t )) for every t in the interval. Example. For which values of r is y ( t ) = e rt a solution of y 00-9 y + 45 y = 0? HOMEWORK: SECTION 1.3...
View Full Document

This note was uploaded on 05/19/2010 for the course M 427K taught by Professor Fonken during the Spring '08 term at University of Texas at Austin.

Ask a homework question - tutors are online