Force, Work, and Energy

Oh and I just noticed that the units of all three are entirely off. The only way for the units to work is if C1 and C2 have the units of velocity. Then I'm really lost, because I have to choose a C1 and C2. ;_;

I don't have time right now to look through the math, but thats probably a realistic conclusion to come to. When you're solving a differential equation, the most common way to solve them is with a set of boundary conditions, like assuming that your particle starts at rest, which you'd use to find the cconstants.