F.5 MATHS

圖片參考：http://i256.photobucket.com/albums/hh172/hkchelsea_united/20101001_1.png


If you have any questions, please feel free to ask!

y=xe^(-x^2)

dy/dx = e^(-x^2) + xe^(-x^2)‧-2x = e^(-x^2)‧[1-2x^2] ----------using product rule

d^2y/dx^2 = e^(-x^2)‧-4x + e^(-x^2)(1-2x^2)‧-2x -----------using product rule
= e^(-x^2) [-4x + (1-2x^2)(-2x)]
= e^(-x^2) (-6x + 4x^3)

(d^2y/dx^2)+[2x(dy/dx)]+4y
= e^(-x^2) (-6x + 4x^3) + 2x[e^(-x^2)‧(1-2x^2)] + 4xe^(-x^2)
= e^(-x^2) [-6x + 4x^3 + 2x(1 - 2x^2) + 4x]----------pull out common factor e^(-x^2)
= e^(-x^2) [-6x + 4x^3 + 2x - 4x^3 + 4x]
= 0

2010-10-01 12:27:24 補充：
Sorry for the unclear presentation, because when I saw your question, I tried to help you as soon as possible, that's why I just type out the solution here.
I should have made a clearer solution for you. Sorry.