38-2E-08S-solutions

38-2E-08S-solutions - Mathematics 38 Exam II 1. (5 points)...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Mathematics 38 Differential Equations Exam II March 10, 2008 1. (5 points) Determine whether the system x = - ty - z + t y = - x t - z t + 1 z = x - ty is linear. If it is linear a. determine whether it is homogeneous, b. determine its order, and c . write it in matrix form. Solution: Yes. a. no. b. 3. c. x y z = 0 - t - 1 - 1 /t 0 - 1 /t 1 - t 0 x y z + t 1 0 or vx = 0 - t - 1 - 1 /t 0 - 1 /t 1 - t 0 vx + t 1 0 . 2. (5 points) Given the o.d.e. ( D 2 - 1) x = t (N) a. Fnd the equivalent system ( S N ) , b. the general solution of (N) is x ( t ) = c 1 e t + c 2 e t - t . You do not need to verify this . Use the general solution of (N) to obtain each component of the general solution of ( S N ) , c . write ( S N ) in matrix form, d. write the general solution of ( S N ) in the form vx = c 1 v h 1 ( t ) + ··· + c n v h n ( t ) + v p ( t ) . Solution: a. b x 1 = x 2 x 2 = x 1 + t . b. b x 1 ( t ) = c 1 e t + c 2 e t - t x 2 ( t ) = - c 1 e t + c 2 e t - 1 .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/01/2008 for the course MATH 38 taught by Professor Any during the Spring '08 term at Tufts.

Page1 / 3

38-2E-08S-solutions - Mathematics 38 Exam II 1. (5 points)...

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