= Solution
The difference of two solutions would satisfy $Ly=0$ with $y(0)=0$, $y'(1)=0$. This would be a zero <eigenvalue> of the homogeneous problem, but part (b) shows there is none. Hence \b[at most one solution exists]. For continuous forcing the standard second-order existence construction also works: the free initial slope is fixed by an equation with coefficient $\cos1\ne0$. Thus for the stated regular boundary-value problem the solution is unique even with nonzero endpoint data.
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