Using the displacement formulation given in Section 9.3.2, use standard separation of variables to solve the torsion

Question:

Using the displacement formulation given in Section 9.3.2, use standard separation of variables to solve the torsion problem of an elliptical section shown in Fig. 9.7. For this problem it is only necessary to use results coming from the zero-separation constant case. Verify your solution with relation (9.4.11).

Fig 9.7