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Reduction of Order Method - Differential Equation Help

  1. Mar 11, 2009 #1
    1. Problem Statement

    Okay so I know these appear to be simple but for some reason I am having trouble finding the methods by which to solve them.

    Problem 1:

    This problem must be solved by reduction of order method and cannot use the y2 formula.

    (1 - x^2)y'' + 2xy' = 0; y1 = 1


    Problem 2:

    This problem must be solved by reduction of order method and cannot use the y2 formula.

    4x^2y'' + y = 0; y1 = [x^(1/2)]ln|x|



    2. Relevant equations

    y2 / y1 = u (x)

    y2 = u (x) * y1 (x)

    y' = u'x + u

    y'' = u''x +2u'


    3. The attempt at a solution

    The general form for the problem is:

    eq0001M.gif


    I have been trying to use Paul's Notes (http://tutorial.math.lamar.edu/Classes/DE/ReductionofOrder.aspx) to help me along the way but I am unable to follow for the lack of the teacher not exactly teaching the problems.


    Any help getting towards the right direction would be much appreciated. Thank you.
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Mar 11, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    For the first one...try putting w=y' such that w'=y''

    Now you have a first order DE.

    For the second one, if y=y1 is a solution, then y=v*y1 is another solution.
     
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