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

PG1995

Joined Apr 15, 2011
816
Hi

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.

Regards
PG

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thatoneguy

Joined Feb 19, 2009
6,359
± since either one satisfies the equation.

1chance

Joined Nov 26, 2011
46
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.