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Keep it real


Hi,

Is there a way to make Mathematica stick to real numbers and functions 
as much as possible? For example, could I somehow get two real function 
solutions to the problem

DSolve[g''[z] + (\[Lambda] Cosh[(z - H/2)/a]^2) g[z] == 0, g, z];



Many thanks in advance,

Sam


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