Given dy/dt=4y and y(2)=200. Find y(9)

Answer 1

dy/dt = 4y
dy/y = 4 dt
lny = 4t + C
y = ce^(4t)
y(2) = 200 means
c*e^8 = 200
c = 200e^-8
y = 200e^-8 * e^(4t) = 200e^(4t-8)
y(9) = 200e^28