which form should I use y = -c|x^3| or y = -c|x^3|

Discussion in 'Math' started by PG1995, Nov 25, 2011.

  1. PG1995

    Thread Starter Distinguished Member

    Apr 15, 2011

    Please have a look on the attachment. I have integrated the "solution" which is a differential equation to see if I get back y just out of curiosity. As you can see, I ended up with:
    1: y = -c|x^3|, or, 2: y = c|x^3|

    The original form was y=c1*x^3. So which form should I use, "1" or "2"? I think it's "2" because the original form didn't have a negative sign "-". But what about the absolute value?

    Let me rephrase it. Both solutions, 1: y = -c|x^3|, or, 2: y = c|x^3|, satisfy the differential equation, dy/dx=3y/x. I started with y=c1*x^3 (let's call "3") which is also a solution to the differential equation in addition to "1" and "2". But when I integrated the differential equation I only ended up with "1" and "2", there was no third solution. Isn't there any difference between y=c|x^3| and y=c1*x^3? I think there is. Please help me with it. Thank you.

  2. thatoneguy

    AAC Fanatic!

    Feb 19, 2009
    ± since either one satisfies the equation.
  3. 1chance


    Nov 26, 2011
    Since "c" stands for constant, as in a number, it is not necessary to worry about the + or -. It will take care of itself depending on the value of c. Standard procedure has one using the positive version, at least that's what I teach my students.