We compute cohomology spaces of Lie algebras that describe
differential invariants of third order ordinary differential equations. We prove
that the algebra of all differential invariants is generated by 2 tensorial
invariants of order 2, one invariant of order 3 and one invariant of order 4.
The main computational tool is a Serre-Hochschild spectral sequence and
the representation theory of semisimple Lie algebras. We compute differential
invariants up to degree 2 as application.
