Concept explainers
The Bessel function of order 0, y = J(x), satisfies the differential equation xy″ + y′ + xy = 0 for all values of x and its value at 0 is J′(0) = 1.
(a) Find J′(0).
(b) Use implicit differentiation to find J″(0).
(a)
To find: The value
Answer to Problem 55E
The value
Explanation of Solution
Given:
The Bessel function of order 0,
Proof:
Obtain the value
Since
Substitute
Therefore, the value
(b)
To find: The value
Answer to Problem 55E
The value
Explanation of Solution
Calculation:
Obtain the value
Since
Differentiate implicitly with respect to x,
Apply the product rule and simplify the terms,
Substitute
Substitute
Therefore, the value
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