(a) Show that J 0 (the Bessel function of order 0 given in Example 4) satisfies the differential equation x 2 J 0 ′ ′ ( x ) + x J 0 ′ ( x ) + x 2 J 0 ( x ) = 0 (b) Evaluate ∫ 0 1 J 0 ( x ) d x correct to three decimal places.
Solution Summary: The author explains how the function J_0 satisfies the differential equation.
(a) Show that
J
0
(the Bessel function of order 0 given in Example 4) satisfies the differential equation
x
2
J
0
′
′
(
x
)
+
x
J
0
′
(
x
)
+
x
2
J
0
(
x
)
=
0
(b) Evaluate
∫
0
1
J
0
(
x
)
d
x
correct to three decimal places.
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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