Question

(a) Show that the function

Answer 1

\[f(x) =\sum_{k=0}^{\infty} \frac{ (-1)^{k} x ^{2k} }{ 2^{2k}(k!)^{2} }\]

Answer 2

satisfies the differential equation
x\[x^{2} f''(x)+xf'(x)+x ^{2}f(x) =0\]

Answer 3

It might be some work, but you clearly want to differentiate the function first, make sure that you also consider the change of index and at the very end also matching them together again.

Answer 4

how to differentiate f(x)

Answer 5

Could you read it?