I have verified that

, so I'm looking for a little more of a suggestion. I tried including the C in the squaring, but this just gave me a crazy answer that also didn't work out correctly. For sure, I might be doing something wrong with that calculation, but my basic source of confusion at this point is how I should "correctly" square the right side of this equation.

Please have a little mercy here. This is my first exposure to differential equations. So far, in all of our integrals, we just leave the C alone, but I think that in this case, I have to do something with it, but I don't know exactly what that is. The bigger question is "when do I leave the C alone and when do I wrap it up in the rest of the algebra?". Are there any rules for this? Our text book doesn't get into this at all, but here it seems to be elemental to solving this.

Thanks for helping me. I'm frustrated, but I appreciate your help.