9231 P12 - Nov 2022 - Q04 - 7 marks
4256
The function \(f\) is such that \(f''(x)= f(x)\)
Prove by mathematical induction that, for every positive integer n,
\(\frac{d^{2n-1}}{dx^{2n-1}}(xf(x)) = xf'(x) + (2n-1)f(x).\)
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