Hello Everyone!

I've recently came across step functions in my systems course, they frequently appear in ODEs describing the system.

An ODE I came across was

. Now, I know I must ask this in the differential equations forum, but, I know what the solution should be, it's just that I'm not "okay" with integrals involving step functions. In the above equation, we would get

but what's

? Shouldn't it be plain

?

If so, when substituting our new solution in the DE, we get:

. How come?!

Any help is appreciated!