- #1

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## Homework Statement

See attached photo

## Homework Equations

## 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:

y'= -sint

y''= -cost

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?

Thanks :)