Question

Diff eq problem. Any help on how to tackle this problem would be greatly appreciated! Not sure where I should even start.

Determine the first order differential equation given the graphical response shown below. Assume the input is a step function 4 t (s)

Answer 1

y (t) = 4 (1 - e^-t) u (t) x (t) = U (t) y (s) = integral_0^infinity y (t) e6-st dt integral_0^infinity 4 (1 - e^-t) u (t) e6-st dt = integral_0^infinity 4 e^-st - 44 integral_0^infinity e^-t e^-st dt = 4/s - 4/s + 1 = 4/s (s + 1) X(s) = integral_0^infinity u (t) e^-s t dt = 1/s Y(s)/X(s) = 4/s (s + 1) times s = 4/s + 1 y(s)/x(s) = 4/s + 1 S y (s) + y (s) = Delta X (s) rightarrow Differential equation is as we know that y (t) y (s) then d y (t)/dt s y (s) Therefore d y (t)/dt + y (t) = 4 x(t)