review1-sol

# review1-sol - MAP2302, FALL 07 EXAM1 To receive full credit...

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

Unformatted text preview: MAP2302, FALL 07 EXAM1 To receive full credit you must carefully explain your answers 1. Determine those m so that φ ( x ) = x m is a solution of x 2 y 00- xy- 3 y = 0 . Problem 21 b section 1.2. With the choice of φ , note that φ = mx m- 1 and φ 00 = m ( m- 1) x m- 2 . Substituting into the differential equation gives, m ( m- 1) x m- mx m- 3 x m = 0 . Thus, x m is a solution if and only if m 2- 2 m- 3 = 0. Thus, m = 3 ,- 1. 2. Does the relation e xy + y = x- 1 determine an implicit solution of y = e- xy- y e- xy + x ? Problem 11 section 1.2. Differentiating the expression implicitly with respect to x gives, e xy ( xy + y ) + y = 1 . Solving for y we find, (1 + xe xy ) y = 1- ye xy which, after rearranging, gives, y = e- xy- y e xy + x . Thus the expression does define an implicit solution to the given dif- ferential equation. 3. Draw some isoclines for y = 2 x 2- y . What is the slope of the solution passing through (0 , 1) at the point (0 , 1)?...
View Full Document

## This note was uploaded on 12/15/2011 for the course MAP 2302 taught by Professor Tuncer during the Spring '08 term at University of Florida.

### Page1 / 3

review1-sol - MAP2302, FALL 07 EXAM1 To receive full credit...

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

View Full Document
Ask a homework question - tutors are online