Thread: differential equation proving

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

Well, it's actually just an error in differentiating:





The first one was an exponential, so we used the chain rule, but notice that this is a product, so we must use the product rule:



Now we do the division:



Which gives:





And there is the right answer.

Thanks for helping me out. Guess I was kinda careless as well. Anyway, thanks again ...