Question

Solve differential equation dy(t) / dt = -2y(t) with initial condition y = 2 when t = 1

Answer 1

y = 2e^[2(1 - t)]

Explanation:

1/y . dy = -2. dt

ln(y) = -2t + c

ln(2) = -2(1) + c

c = 2 + ln(2)

ln(y) = -2t + ln(2) + 2

ln(y) - ln(2) = 2 - 2t

ln(y/2) = 2 - 2t

y/2 = e^(2 - 2t)

y = 2e^[2(1 - t)]