[QUE/CM-01004] Periodic Motion $ F = -k x +{ \lambda\over x^3} $ (with solution)

Question : A particle in one dimension is subject to a force
$$ F = -k x +{ \lambda\over x^3} $$
Find the potential energy and the exact period of oscillations for
$\lambda = 6ka^4, E= 5k a^2$.