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## Homework Statement

Lets say for example, we are given:

dy/dx - 4y = 2 or y' - 4y = 2 , y(0) = 4

=> M= e^(-4t)

e^(-4t) y' - 4e^(-4t)y = 2 e^(-4t)

e^(-4t) y = -1/2 [ e^-4t ] + C

y = -1/2 + Ce^4t

When t = 0, y = 4

4 = -1/2 + C

C = 4.5

therefore... y = -1/2 + 4.5e^4t

Now, is -1/2 the null function or particular? what about for 4.5e^4t?

I was imagine a long period of time before the "system" starts, so t = negative infinity, then the exponential function would approach 0, and we would be left with y = -1/2

if t = 0, when the system just starts, we were given y = 4

now after a very long period of time, t = infinity

y = infinity

What does this mean? the system has no steady state?