BITSAT Mathematics Question (2024) — Solution

Step-by-step solution

Given differential equation is d p(t) d t =0.5 p(t)-450 d p(t) d t = 1 2 p(t)-450 d p(t) d t = p(t)-900 2 2 d p(t) d t =-[900-p(t)] 2 d p(t) 900-p(t) =-d t Integrate both the side, we get : -2 d p(t) 900-p(t) = d t Let 900-p(t)=u -d p(t)=d u We have; 2 d u u = d t 2 u=t+c 2 [900-p(t)]=t+c when t=0, p(0)=850 2 (50)=c 2 [ ( 900-p(t) 50 ) ]=t 900-p(t)=50 e^ t 2 p(t)=900-50 e^ t 2 let p (t_1 )=0 0=900-50 e^ t_1 2 t_1=2 18