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

Question

Mathematics

Mikayla Donovan

3 May, 11:32

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

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Answers (1)

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Savanah Stein · Answer 1

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) ]