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Confusion about integration constant

  1. Jun 14, 2013 #1
    After solving a DE I ended up with (y3)/(3x3) + ln(x) = c and initial conditions y(1) = 2.

    If I just plug in straight away I get (23) / (3(13)) + ln(1) = c which is c = 8/3 but if I multiply the equation by 3x3 first: (y^3) + (3x3)ln(x) = (3x3)c and the 3 goes into the c and solving for c I get 23 + 3(1)3ln(1) = (1)3c and c = 8 which is the right answer.

    I can see why these answers are different but I don't think I understand the constant. If I don't combine other constants with c I get an incorrect answer? When can I/do I have to combine constants with c?
  2. jcsd
  3. Jun 14, 2013 #2
    When you did it by the second method, you were missing a factor of 3 as the coefficient of c.
  4. Jun 14, 2013 #3
    Oh, that was because I combined it with the c.
  5. Jun 14, 2013 #4
    Solution 1: (y^3)/(3x^3) + ln(x) = 8/3

    Solution 2: (y^3) + (3x^3)ln(x) = 8(x^3)

    No difference!!
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