$\"\"$

\

The Bessel function of first order equation is $\"\"$ .

\

$\"\"$

\

Apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Again apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

(a)

\

Consider differential equation is $\"\"$ .

\

Substitute $\"\"$ , $\"\"$ and

\

$\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Consider $\"\"$ .

\

$\"\"$ .

\

Consider $\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

(b) Show that $\"\"$ .

\

The Bessel equation is $\"\"$ .

\

$\"\"$

\

Apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

(a) $\"\"$ .

\

(b) $\"\"$ .