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Abel's Equation and Wronskian for find out y2

  1. Apr 24, 2016 #1
    1. The problem statement, all variables and given/known data
    x²y''+xy'+(x²-0,25)y=0
    y1= x^-1/2*sin x


    2. Relevant equations
    Abel's equation:
    W= c.e^-(integrate (p(t))


    3. The attempt at a solution

    My Wronskian gave me a first order ODE that I really don't know solve.

    x^-1/2*sinx y' + (1/2 x^-3/2 sin x- x^-1/2cosx) y2

    I don't solved the Abel's equation cause I don't know what to do with this amount of sin and cos ahahhahaha.

    Is the exercise 37 of Boyce and Diprima
     
  2. jcsd
  3. Apr 26, 2016 #2
    Since you are given one solution you should use the method of reduction of order to find the other one, and it should be in the chapter where you found the question (did it myself a few months ago).
     
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