soln11 - ECE320 Solution Notes 11 Spring 2006 Cornell...

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

Unformatted text preview: ECE320 Solution Notes 11 Spring 2006 Cornell University T.L.Fine 1. Classify the following ode s as to whether they are autonomous and what their orders and degrees are: ( a ) ¨ x + ω 2 x = 0 , harmonic oscillator; ( b ) ¨ x- tx = 0 , Airy ode; ( c ) t 2 ¨ x + t ˙ x + ( λ 2 t 2- n 2 ) x = 0 , Bessel’s equation; ( d ) ˙ x- tx 2 = e- t ; ( e ) tan(¨ x )- x = 0; ( f ) ¨ x ˙ xx = sin( t ); ( g ) ( ˙ x ) 2- x = 0; ( h ) ¨ x =- x 2 + sin( ω ˙ x ) . 1. autonomous, order 2, degree 1. 2. nonautonomous, order 2, degree 1. 3. nonautonomous, order 2, degree 1. 4. nonautonomous, order 1, degree1. 5. autonomous, order 2, degree infinity. 6. autonomous, order 2, degree 1. 7. autonomous, order 1, degree 2. 8. autonomous, order 2, degree 1. 2. Represent each of the ode s of Problem 1 in the standard form ˙ y = F ( y ), if possible. ( a ) y 1 = x, y 2 = ˙ x, ˙ y 1 = y 2 , ˙ y 2 =- ω 2 y 1 ; ( b ) y = t, y 1 = x, y 2 = ˙ x, ˙ y = 1 , ˙ y 1 = y 2 , ˙ y 2 = y y 1 ; ( c ) y = t, y 1...
View Full Document

This homework help was uploaded on 09/25/2007 for the course ECE 3200 taught by Professor Fine during the Spring '06 term at Cornell.

Page1 / 3

soln11 - ECE320 Solution Notes 11 Spring 2006 Cornell...

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

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