• Callisto
Given that $$y=x^2cosx$$ satisfies $$x^2y^{(2)} - 4xy^{(1)} + (x^2 +6)y =0$$ , where $$y^{(n)} = \frac{d^ny}{dx^n}$$. (a) Show that when x=0, $$(n-2)(n-3)y^{(n)} = -n(n-1)y^{(n-2)}$$. (b) If we use the notation $$\bar y^{(n)} = \frac{d^ny}{dx^n}|_{x=0}$$, find $$\bar y^{(2m)}$$ and $$\bar y^{(2m+1)}$$. How to do part (b)?
Mathematics

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