Answer:
(a) The solution to the differential equation is x = A_0Coswt + Ce^(-kx)
(b) The initial condition t > 0 will not make much of a difference.
Step-by-step explanation:
Given the differential equation
dx/dt= −k(x − A); t > 0, A = A_0Coswt
(a) To solve the differential equation, first separate the variables.
dx/(x - A) = -kdt
Integrating both sides, we have
ln(x - A) = -kt + c
x - A = Ce^(-kt) (Where C = ce^(-kt))
x = A + Ce^(-kx)
Now, we put A = A_0Coswt
x = A_0Coswt + Ce^(-kx) (Where C is constant.)
And we have the solution.
(b) Since temperature t ≠ 0, the initial condition t > 0 will not make much of a difference because, Cos(wt) = Cos(-wt).
It is not any different from when t < 0.
