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
Unformatted text preview: Practice Exam 1, 2/15/2012, Math 244 Diff. Eq.s, Prof. Tumulka 1 2 3 4 5 6 7 8 9 10 11 Σ Name: Given formula: The general solution of the first order linear ODE y + p ( t ) y = g ( t ) is y ( t ) = 1 μ ( t ) Z μ ( t ) g ( t ) dt + c , μ ( t ) = e R p ( t ) dt Calculators, books and notes are not allowed. Good luck! 1) [worth 4 points out of 100] True or false? The global truncation error in the Runge– Kutta method has an upper bound proportional to (Δ t ) 5 . 2) [4 points] In which case does one say that the DE y 00 + p ( t ) y + q ( t ) y = g ( t ) is homogeneous? 3) [7 points] a) What does the “superposition principle” say? b) To which of the following DEs does it apply? (i) y 00 4 y = sin t yes no (ii) y 00 + (sin t ) y 4 y = 0 yes no (iii) y 00 4 y + sin y = 0 yes no 4) [5 points] Determine the longest interval in which the IVP ( t 1) y 00 3 ty +4 y = sin t , y ( 2) = 2, y ( 2) = 1 is certain to have a unique solution. Do not attempt to find the solution....
View
Full
Document
This note was uploaded on 02/27/2012 for the course MATH 640:244 taught by Professor Ming during the Spring '09 term at Rutgers.
 Spring '09
 Ming

Click to edit the document details