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(1) One can use either solution_dict=True... or the rhs method...
sage: h_sol = solve(eq_sol, h, solution_dict=True)[0][ h(t) ]
sage: h_sol
1/3*sqrt(3)*sqrt(c1)*(e^(2/3*sqrt(3)*_C*sqrt(c1) + 2/3*sqrt(3)*sqrt(c1)*t) + 1)/(e^(2/3*sqrt(3)*_C*sqrt(c1) + 2/3*sqrt(3)*sqrt(c1)*t) - 1)
sage: h_sol = solve(eq_sol, h)[0].rhs()
sage: h_sol
1/3*sqrt(3)*sqrt(c1)*(e^(2/3*sqrt(3)*_C*sqrt(c1) + 2/3*sqrt(3)*sqrt(c1)*t) + 1)/(e^(2/3*sqrt(3)*_C*sqrt(c1) + 2/3*sqrt(3)*sqrt(c1)*t) - 1)
(2) The human eye can do this better, just divide by the exponential of the half exponent. For me, the delivered form is acceptable, rational function composed with exponential function.
(No simplify.... method gave me an other expression.)
