Help with a simple first order differential equation that seems to contradict itself.
So given a differential equation that models the mass of a substance (m) produced during a chemical reaction after time (t).
equation: dm/dt = (50-m)²/500 (given m=0 when t=0)
after i solved it, i get: m = (50) + (500/(t-10))
but this looks problematic.
firstly it implies that the substance keeps getting smaller mass, shouldn't m be getting bigger as t does?!?!?!?
secondly, during the first 10 seconds the mass is negative!
and also t can never equal 10 then!!! (denominator will be 0).
and lastly, i'm asked to show that the mass will never exceed 50...but wait isn't it ALWAYS going to be bigger than 50?!?! it never gets below 50!.
please help or show me what i did wrong, so appreciated thanks!!!!