stable steady-state value
Solve the following linear, first-order differential equations and ensure that the initial conditions are satisfied. Show whether or not the steady-state solutions are stable.
(a) 10y’ = 5y and y(0) = 1. The answer is y(t) = e^(1/2t), but having trouble arriving at that answer
(b) 4y’ – 4y = -8 and y(0) = 10. The answer is y(t) = 8e^t + 2 , but having trouble arriving at the answer
(c) y’ + 2y = 4 and y(0) = 3
(d) Draw and describe a phase diagram for one of the above equations with a stable steady-state value.