This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MATH 24Exam 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 24Exam 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.
 Spring '10
 Yatzkar
 Differential Equations, Equations, Approximation

Click to edit the document details