#### Problem 61E

61. The Bessel function of order $0, y=J(x)$, satisfies the differential equation $x y^{\prime \prime}+y^{\prime}+x y=0$ for all values of $x$ and its value at 0 is $J(0)=1$.

(a) Find $J^{\prime}(0)$.

(b) Use implicit differentiation to find $J^{\prime \prime}(0)$.