Editing 128: dPain over dt
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==Explanation== | ==Explanation== | ||
| − | Another one of the math-love relationship comics, a mathematical depiction of pain as a {{w|differential equation}} is shown. It is hoped that ''dPain/dt'', or the rate of pain (in this case, shrinking), decreases quickly so that the pain will vanish quickly. He's hoping the value for ''d'' will not be larger than a few days or some weeks. Assuming that ''How much she's still in my life'' is a constant [Megan], [ | + | Another one of the math-love relationship comics, a mathematical depiction of pain as a {{w|differential equation}} is shown. It is hoped that ''dPain/dt'', or the rate of pain (in this case, shrinking), decreases quickly so that the pain will vanish quickly. He's hoping the value for ''d'' will not be larger than a few days or some weeks. Assuming that ''How much she's still in my life'' is a constant [Megan], [http://www.wolframalpha.com/input/?i=dP%2Fdt+%3D+%28-k1*P%2BG%29*%281%2F%281%2Bexp%28-%28t-k2%29%2Fd%29%29%29 solving the differential equation] leads to the following solution (with unknown ''c<sub>1</sub>''): |
: <math> Pain(t) = {c_1 \left(e^{k_2/d} + e^{t/d}\right)}^{-dk_1} + \frac{[\text{Megan}]}{k_1}</math> | : <math> Pain(t) = {c_1 \left(e^{k_2/d} + e^{t/d}\right)}^{-dk_1} + \frac{[\text{Megan}]}{k_1}</math> | ||
