If xy=cos2x,show that d2y dy
x ---- + 2 ----- + 4xy =0
dx2 dx
A-maths 問題!!!
2006-11-18 10:12 pm
回答 (1)
2006-11-18 10:18 pm
✔ 最佳答案
xy=cos2xdifferentiate
d(xy)/dx=d(cos2x)/dx
differentiate once more time
x(dy/dx)+y=-2sin2x
x(d^2y/dx^2)+dy/dx+dy/dx=-4cos2x
x(d^2y/dx^2)+dy/dx+dy/dx+4cos2x=0
x(d^2y/dx^2)+2(dy/dx)++4xy=0
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