09fall2

# 09fall2 - MTH 108 Fall 09-10 Exam 2 Show all work Justify...

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

MTH 108 Fall 09-10 Exam 2, Show all work. Justify procedures and calculations except when they are obvious as, for example, when you integrate both sides of an equation. When doing so, use complete, grammatically correct sentences. No books, notes, calculators. 1. (a) Find a solution of the third order ODE in the half-line 0 < x < , u ±±± + 8 u = 0 , which satisﬁes the conditions that u (0) = 5 and that u ( x ) decays to zero as x tends to inﬁnity. Do you think the solution is unique? (b) Find the general solution of the third order ODE u ±±± + 4 u ± = 0 2. Let the real valued functions f ( x ) and g ( x ) be deﬁned, in 0 < x < 1, by f ( x ) = a 1 φ 1 ( x ) + a 2 φ 2 ( x ) + a 3 φ 3 ( x ) + ··· , g ( x ) = b 1 φ 1 ( x ) + b 2 φ 2 ( x ) + b 3 φ 3 ( x ) + ··· , where φ 1 , φ 2 , φ 3 , ··· is a given orthonormal basis of real valued functions in the interval 0 < x < 1, with inner (dot) product ( f, g ) = Z 1 0 f ( x ) g ( x ) dx. (a) Prove that

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 01/17/2010 for the course MATH 108 taught by Professor Trangenstein during the Fall '07 term at Duke.

### Page1 / 2

09fall2 - MTH 108 Fall 09-10 Exam 2 Show all work Justify...

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

View Full Document
Ask a homework question - tutors are online