Hello Everyone!

I'm trying to recall the basics of ODEs, I'm using that in my systems course. Suppose, we have an equation:

$\displaystyle y'+y=f(x)$

The solution would be 2 contributions, the solution to the homogenous equation and the particular solutions, now my questions are:

(1) Does the particular solution have to be of the form $\displaystyle f(x)$?

(2) Take $\displaystyle f(x)$ to be the unit step function $\displaystyle u(x)$, what would then the solution be?

Thanks for the help?