See attached photo
The Attempt at a Solution
I don't even know where to start on this problem. Usually, if I am given a possible solution to a DE, say y(t)=cos(t) as a solution to y''-y'+y=sin(t), I find whether it was a solution or not by manipulating it and then plugging it into the second equation that it may be a solution to and then seeing whether the resulting statement is true. For the ex. problem I give in this section, I would do this:
then sub them in: -cost +sint +cost = sint
and by simplifying get: sint = sint
so for this case, it y=cost is a solution.
But with the problem that is in the attached photo I have no idea what to do.
Does anyone have an guidance as to how I can solve the attached problem?