= Solution
{c}
Putting both data at zero makes this an <initial value problem>. The <uniqueness theorem for ordinary differential equations> applies, and one can also prove uniqueness directly: the difference of two solutions is a <homogeneous solution> $A\cos x+B\sin x$ whose value and first <derivative> at zero are both zero, forcing $A=B=0$. In fact, for every prescribed <continuous function> $f$,
$$
\boxed{y(x)=\int_0^x\sin(x-t)f(t)\,dt}
$$
satisfies both initial data and $y''+y=f$. Consequently non-uniqueness is impossible for every $l>0$, including $l=m\pi$. In this setting the <kernel> is trivial. The <boundary conditions> at a single endpoint do not give the same <self-adjoint operator> domain as the two separated <Dirichlet boundary conditions>, so the earlier exceptional lengths do not apply.
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