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pochemuha
3 years ago
14

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

Mathematics
1 answer:
juin [17]3 years ago
6 0

Answer:

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

Step-by-step 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)]

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