Could you plz help me or give me any hint to solve this ODE..(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{d^2y}{d x^2} + ( 2\rm{sech}^2 x - a^2 ) y = 0[/tex]

where a is a constant.

I want only even function solution. (y(x) = y(-x))

BTW, this is a homework problem. I encountered this equation while considering surface waves in a self-gravitating incompressible fluid with stratification.

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# Second order ODE

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