= Solution
At an ordinary point, an order-$n$ <linear ordinary differential equation> has $n$ arbitrary constants in its general solution. Determining them uniquely requires $n$ independent, consistent scalar conditions. Prescribing $y,y',\ldots,y^{(n-1)}$ at one ordinary point gives uniqueness under the standard continuous-coefficient assumptions. Conditions at different endpoints need an additional nonsingularity check: for example, $y''+y=0$, $y(0)=y(\pi)=0$ leaves every multiple of $\sin x$ possible. Thus counting <boundary conditions> alone does not guarantee uniqueness for a <boundary value problem>.
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