Love Vs Sanity

Let S: Sanity Level
L: Level of love input
t : Time

dS/dt = -kL , k=constant

Let L = a - 1/(t+b) ,
Reason for equation of L: Level of love input must increase at a decreasing rate, and i believe there is an upper bound for it(asymptote).

Substitute and solving,

S = k(-at + ln(t+b) ) +c
Shape of graph: An inverted U shape with a max point at 1/a-b. c is a constant chosen to ensure S>0 for t>0.

Initial love input at t=0 : a- 1/b
max point of S vs t : t=1/a - b ( sanity breakdown point!)

When a is high, Initial love input is high, the t when max point of S occurs is probably at negative region. Which means.... ur sanity just simply keeps dropping, AKA Complete obsession.

When b is high instead, initial love input fairly low, unfortunately the max point of S still in negative region, so there is no difference from previous case. This is Eventual complete obsession!

Conclusion: You will lose your sanity eventually in the game of love! That is why Love leech every bit of sanity out of you!

This is what i thought of when i was travelling in train. LOL! Did all the maths and deduction in my mind. Just purely for fun.... Hope no one offended.