Find the solution to the differential equation dydt 05 y 20

Solution

dy/dt= 0.5 (y 200)
if y=30 when t=0.

dy/(y-200) = 0.5 dt

take integration

ln(y-200) = 0.5t +C

y-200 = e^0.5t C

y = 200 + K e^0.5t

t = 0 y = 30

30 = 200 + K

K = 30 - 200 = -170

y = 200 -170 e^0.5t