p=ed(\phi_2^2-\phi_1^2)=ed(\frac{(1-\eta)^2}{2(1-\eta)}-\frac{1}{2(1-\eta)})=-ed\frac{\eta}{2(1-\eta)}
But the answer model tells p=-ed \frac{\eta}{1-\eta}, therefore I think a factor 1/2 is missing.
Thank you for the question. Note that \phi_2^2=1-\phi_1^2.
This would give \phi_2^2-\phi_1^2 =1- 2\phi_1^2 = 1-\frac{1}{1-\eta} = \frac{-\eta}{1-\eta} so the model answer seems correct ?