Diferential Equation- please answer as soon as possible please 2. A chicken in t

Question

Diferential Equation- please answer as soon as possible please

2. A chicken in taken out of the tree ter (onco and plaeed on a table in a 20 C room. Five minutea later the is rc It warms according to Newton's law. what the temperature of the chicken ia after 30 minutes? 3. Determine whether the given tunctiona are 1inearly independent or independent on (-oo, oo). 4. verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval Form the general solution yet on (-oo,oo). yi

Explanation / Answer

Solution:2

Let T denote the temperature of the chicken
after a time t minutes. The constant room
temperature is Tm = 20°C.

therefore
dT/dt = k(Tm-T)

dT/dt = k(20 T)

now

Let be the difference in temperature
between the room temperature and the chicken

= 20 -T

d/dt = k

Solution of this equation

= oekt

To determine the value of o, use the
given initial conditions.

Initially, t = 0 and T0 = 0°C.
= Tm T0
= 20 - 0
= 20

To determine the value of k, use the other
given condition.

When t = 5, T = 2°C, so
(5) = 20 2
= 18

Substitute in the given values.

in = oekt

18=20 ek*5

k = -0.021

Write the solution of the differential equation. (t) =0e-0.021*t

Plug t = 30 to determine the

temperature after a further 30 minutes

(30) =0e-0.021*30

(30) =20e-0.021*30 = 10.65 C

Answer

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