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## Main Question or Discussion Point

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.