ode internal name "second_order_bessel_ode_form_A"
These are ode of the above form which can be converted to Bessel using transformation
4.3.2.15.1 Example
can be transformed to Bessel ode using the transformation
Where
And
Substituting (2,3) into (1) gives
Which is Bessel ODE. Comparing the above to the general known Bowman form of Bessel ode which is
And now comparing (4) and (C) shows that
(5) gives
But the solution to (C) which is general form of Bessel ode is known and given by
Substituting the above values found into this solution gives
Since
Equation (9) above is the solution to
Comparing the above to
Another example for illustration. Given the ode
Comparing the above to
Another example for illustration. Given the ode
Comparing the above to