Discussion
An nth order linear ordinary differential equation :
Answer: A
The answer is has exactly \(n\) linearly independent solutions.
For a homogeneous linear equation \(y^{(n)} + a_{1}(x)y^{(n-1)} + \cdots + a_{n}(x)y = 0\) with continuous coefficients, the solution set is a vector space of dimension exactly \(n\). The existence-uniqueness theorem gives \(n\) independent solutions (one for each choice of initial data \(e_{1}, \ldots, e_{n}\)), and any \(n + 1\) solutions are dependent.
The paper does not say 'homogeneous', but that is the standard textbook statement it rests on. 'At most \(n\)' and 'minimum \(n\)' are each half of the truth, and 'less than \(n\)' is false.
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