Exam1_M24_soln_S10

# Exam1_M24_soln_S10 - MATH 24-Exam 1 Spring 2010 Solution(1...

This preview shows pages 1–3. 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: MATH 24-Exam 1 Spring 2010 Solution (1) For IVP y = y (3 t- 1) , y (0) = 2 find Euler approximate solution at t=1 using step size h = 0 . 5 . Do you see any problems with this approximation? Euler’s formula is y n +1 = y n + hf ( t n ,y n ) and t n +1 = t n + h t y y 2- 2 . 5 1 2 1 2 y (1) ≈ 2 although this approximation is incorrect because y’ is undefined at t = 1 3 and with the step size of .5 we’re stepping right over the singularity. (2) Match each of the following differential equations with one of the direction fields. (3pts each) ( i ) d y d t = y ( y 2- π 2 ) → (B) ( ii ) d y d t = t (2- y ) → (A) Equilibrium point at y = 2 as opposed to the isocline at t = 2 in (iii) ( iii ) d y d t = y (2- t ) → (D) ( iv ) d y d t = sin y → (C) Unstable equilibrium at y = 0 as opposed to stable at y = 0 in (i) (A) (B) (C) (D) MATH 24-Exam 1 Spring 2010 (3) Consider IVP ty- 3 y = t 4 , y (1) = 4 a. What does the Picard’s Theorem tell you for this problem?...
View Full Document

## This note was uploaded on 11/23/2010 for the course MATH 024 taught by Professor Yatzkar during the Spring '10 term at UC Merced.

### Page1 / 3

Exam1_M24_soln_S10 - MATH 24-Exam 1 Spring 2010 Solution(1...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online