# Perhaps delta function or inverse Laplace transform?

Hello everyone,
i have this question and not even sure how to approach it:

$$\frac {di}{dt}+4i+3\int_{0^-}^t{i(z)dz = 12(t-1)u(t-1)$$

and $$i(0^-) = 0$$

find $$i(t)$$

last topics we covered were laplace transforms (and inverse) and dirac delta function.
At least some hint to get me started would be a great help.

EDIT:
oh, and again u(t) = 1 for t >= 0 and u(t) = 0 elsewhere.

Last edited:

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BobG
Homework Helper
I would get rid of the integral by taking the derivative of the entire equation - which gives you a second order differential equation and leads you into the LaPlace transform.

Tide
Homework Helper
Laplace transform the equation directly. To find the transform of the integral, just do an integration by parts. That will avoid complications on the right side. :)

thanks for replies, as i looked further through the book, we actually have an entry in the table for this integral, but what do I do with $$i$$ for Laplace transform? it does not have u(t)...

Tide