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4 Questions on Ordinary Differential Equation - Homework 5 | MATH 365, Assignments of Differential Equations

Millersville University of Pennsylvania (MU)Differential Equations
Prof. J. R. Buchanan

Material Type: Assignment; Professor: Buchanan; Class: Ordinary Differential Equation; Subject: Mathematics; University: Millersville University of Pennsylvania; Term: Fall 2008;

Typology: Assignments

Pre 2010

Uploaded on 08/19/2009

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Millersville University Name
Department of Mathematics
MATH 365, Ordinary Differential Equations, Homework 05
October 1, 2008
Answer the following questions by solving the appropriate second order differential equa-
tions. Answers without justifying work will receive no credit. Partial credit will be given
as appropriate, do not leave any problem blank. Each problem is worth 10 points. Your
completed assignment is due at class time on Friday, October 3, 2008.
1. Solve each of the following ODEs and IVPs.
(a) y′′ −3y′+ 2y= 0
(b) y′′ + 2y′+ 5y= 0
pf3
pf4
pf5

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Download 4 Questions on Ordinary Differential Equation - Homework 5 | MATH 365 and more Assignments Differential Equations in PDF only on Docsity!

Millersville University Name Department of Mathematics MATH 365, Ordinary Differential Equations, Homework 05 October 1, 2008 Answer the following questions by solving the appropriate second order differential equa- tions. Answers without justifying work will receive no credit. Partial credit will be given as appropriate, do not leave any problem blank. Each problem is worth 10 points. Your completed assignment is due at class time on Friday, October 3, 2008.

  1. Solve each of the following ODEs and IVPs. (a) y′′^ − 3 y′^ + 2y = 0

(b) y′′^ + 2y′^ + 5y = 0

(c) y′′^ − 4 y′^ + 4y = 0, y(0) = 2, y′(0) = 1.

(d) 4y′′^ − 4 y′^ + y = 0, y(1) = 0, y′(1) = 1.

  1. Consider the IVP y′′^ + 2ay′^ + (a^2 + 1)y = 0 y(0) = 1 y′(0) = − 1 If a = π find the smallest value of T such that |y(t)| < 1 /100 for all t > T.
  1. Find the general form of the Wronskian for the ODE t^2 y′′^ + t cos(ln t)y′^ + (t^2 − n^2 )y = 0 where n ∈ N.