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Third Midterm Exam Problems - Differential Equations | MATH 441, Exams of Differential Equations

University of Illinois - Urbana-ChampaignDifferential Equations

Material Type: Exam; Class: Differential Equations; Subject: Mathematics; University: University of Illinois - Urbana-Champaign; Term: Fall 2006;

Typology: Exams

Pre 2010

Uploaded on 03/16/2009

koofers-user-8l6
koofers-user-8l6 🇺🇸

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Math 441 (E13) – Third Midterm Exam
December 1, 2006
1. (25 points) Solve the differential equation
y00 +xy0+ 2y= 0
by means of a power series about the point x0= 0.
2. (25 points) Find two linearly independent solutions of the differential
equation
xy00 +y0
−y= 0
about x0= 0.
3. (25 points) Find all values of βfor which all solutions of
x2y00 +βy = 0
approach zero as x→0.
4. (25 points) Determine the general solution of the differential equation
4x2y00 + 8xy0+ 17y= 0
that is valid in any interval not including the singular point.
pf3
pf4
pf5

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Math 441 (E13) – Third Midterm Exam

December 1, 2006

  1. (25 points) Solve the differential equation

y′′^ + xy′^ + 2y = 0 by means of a power series about the point x 0 = 0.

  1. (25 points) Find two linearly independent solutions of the differential equation xy′′^ + y′^ − y = 0 about x 0 = 0.
  2. (25 points) Find all values of β for which all solutions of

x^2 y′′^ + βy = 0 approach zero as x → 0.

  1. (25 points) Determine the general solution of the differential equation

4 x^2 y′′^ + 8xy′^ + 17y = 0 that is valid in any interval not including the singular point.