Originally Posted by

**MrMaths**
This exercise is about input and output signals, with the following formula given:

. . . . .[tex]\dfrac{dy}{dt}\, +\, y\, =\, \dfrac{dw}{dt}[/tex]

How could *f*(*t*)* δ*′(*t*) be simplified?

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*.
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