- #1
ozone
- 122
- 0
I was working on a simple differential problem which caused me some confusion
original eq =
dy/dx = -x/2y
which can easily be altered into
y dy = (-x/2) dx
This finally transforms into (after antiderivatives are determined)
(y^2/2) = -(x^2/4) + c
While I can see that this logically is equivallent to the problem above I just don't see how the answer was derived. The x side of the equation makes perfect sense to me, but what I can't tell is how the y was derived to be (y^2/2). In my mind it should have just been y...
That aside I can see that the transformation is logical, but I can't figure out how it was derived.
Thanks,
Ozone.
original eq =
dy/dx = -x/2y
which can easily be altered into
y dy = (-x/2) dx
This finally transforms into (after antiderivatives are determined)
(y^2/2) = -(x^2/4) + c
While I can see that this logically is equivallent to the problem above I just don't see how the answer was derived. The x side of the equation makes perfect sense to me, but what I can't tell is how the y was derived to be (y^2/2). In my mind it should have just been y...
That aside I can see that the transformation is logical, but I can't figure out how it was derived.
Thanks,
Ozone.