Well, in Mathematica you'd type the following command (I'm assuming this is a differential equation, right?):

DSolve[(t H''[t])^2==(H'[t](2n+t+lambda)-H[t])^2-4(t H'[t]-H[t]+delta)((H'[t])^2+lambda H'[t]),H[t],t]

You should double-check that notation, however, and make sure it's correct against your DE. In particular, I'm not sure whether you meant H'[t](2n+t+lambda) or H'(2n+t+lambda).

I don't think Mathematica is going to be able to handle that. At least, my copy of Mathematica 4 can't handle it. Maybe more recent versions have more powerful solvers. I'm talking here about exact, closed-form solutions. Mathematica can probably get you a numerical solution the same as MATLAB or any other solver routine. Do you need a numerical solution?