Given a differential equation

y"= -(2g'/g)y' + [V-E-(g"/g)]y

V(x)= x^(2k) & g(x) = exp(-βx^2/2)

subtitute V(x) & g(x), found

y" = 2βxy' + [x^(2k) - (βx)^2+ β- E]y

the problem i encounter is the subtitution I done is missing β

y" = 2βxy' + [x^(2k) - (βx)^2 - E]y

P/s: ^ represent power of