You need an initial condition to resolve the constant.

In this case I would assume that h(0) = 0.

Substituting the constant in you can solve for zero.

The LaTeX commands you want are \ln{x} for

and \frac{1}{2} for

and for subscripts a_n for

to adjust bracket size use the following commands:

\left[ and \right] so becomes

So your formulas become: