Diff-EQ: integrating factors - signals (how could f(t)δ′(t) be simplified?)
Hey!
I'v been stuck now for a while and found this forum - I hope you guys could help.
The question is: how could f(t)δ′(t) be simplified? And this is about input and output signals.
The given formula from the question: dy/dt + y = dw/dt
They gave me two hints:
1) Use integrating factors
2) There is a integration constant which you could determine since the system is causal
My solution (that I believe is wrong):
I believe the integrating factor is e^t since we have 1*y.
Step 1: d/dx*(y*e^t) = dw/dt * e^t
Step 2: y*e^t = integral | dw/dt * e^t dt = e^t + c
Step 3: y * e^t = e^t + c
Step 4: y = 1 + c*e^-1
The confusing part is step 2. The integral of dw/dt. I believe this is my issue right there.
Also I fail to see how I could reach f(t)δ′(t) from here. I know y = Sw.
Any help would do. Thanks!
Hey!
I'v been stuck now for a while and found this forum - I hope you guys could help.
The question is: how could f(t)δ′(t) be simplified? And this is about input and output signals.
The given formula from the question: dy/dt + y = dw/dt
They gave me two hints:
1) Use integrating factors
2) There is a integration constant which you could determine since the system is causal
My solution (that I believe is wrong):
I believe the integrating factor is e^t since we have 1*y.
Step 1: d/dx*(y*e^t) = dw/dt * e^t
Step 2: y*e^t = integral | dw/dt * e^t dt = e^t + c
Step 3: y * e^t = e^t + c
Step 4: y = 1 + c*e^-1
The confusing part is step 2. The integral of dw/dt. I believe this is my issue right there.
Also I fail to see how I could reach f(t)δ′(t) from here. I know y = Sw.
Any help would do. Thanks!