Hello Everyone!

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

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 ?

(2) Take to be the unit step function , what would then the solution be?

Thanks for the help?