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 = cx^3, or, 2: y = cx^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 = cx^3, or, 2: y = cx^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=cx^3 and y=c1*x^3? I think there is. Please help me with it. Thank you.
Regards
PG
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 = cx^3, or, 2: y = cx^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 = cx^3, or, 2: y = cx^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=cx^3 and y=c1*x^3? I think there is. Please help me with it. Thank you.
Regards
PG
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