Talk:128: dPain over dt
Explanation
- Since this is my first real contribution here I'm putting everything on the talk page instead of on the article itself.
The equation describes Pain as a function of Pain, time, and several constants. This is a first-order linear differential equation with possible solution:
Pain = c_1 (e^k_2 + d e^t)^(-k_1) + (Girl)/k_1
Hopefully, d is relatively small ("days... or weeks"), thereby diminishing the time it takes for Pain to change. Significantly, k_1 needs to be positive, otherwise the first term would grow unbounded and Pain would never decrease. Assuming k_1 is positive, a large k_2 would help ensure the first term shrinks quickly. The "Girl" term guarantees there will always be a certain amount of Pain, unless "How much she's still in my life" is zero.
