Assuming that the first item was 1/(6 x) , this differential equation can be easily solved by the method of separation of variables.
Rewrite it as : dy/ y = 6x sqrt(3 x2 -1) dx
Integrate both sides
ln(y ) =(2/3) (3 x2 -1)3/2 +C
Then y = A exp( (2/3) (3 x2 -1)3/2 )
Where A is a constant of integration