Problem related to bessel functions and sturm-liouville

Question

Bessel Functions and Sturm-Liouville Problem

Response to the following question:

Use the following table to solve 1 and 2.

J₀(x)                 J₁(x)                 Y₀(x)               Y₁(x)

2.4048              0.0000              0.8936              2.1971

5.5201              3.8317              3.9577              5.4297

8.6537              7.0156              7.0861              8.5960

11.7915            10.1735            10.2223            11.7492

14.9309            13.3237             13.3611           14.8974

1. Find the first four α i 0 defined by J1( 3α ) = 0

2. Find the first four α i 0 defined by J'0( 2α ) = 0.