由 --- 於 星期二 五月 06, 2003 6:07 pm
2nd-order estimation:
1/y=y'+y"/2
dx=ydy+ ydy'/2
x+c=yy/2+$ ydy'/2
y~ sqrt(2x+2c)
y'~ 1/sqrt(2x+2c)=1/y
so, $ ydy'/2~lny/2'~ -ln(2x+2c)/4
x+c~yy/2-ln(2x+2c)/4
y~sqrt(2x+2c+ln(2x+2c)/2)
y1=5.2~sqrt(2+2c+ln(2+2c)/2)
c=11.71109441
y ~ sqrt(2x+23.42218882+ln(2x+23.42218882)/2)
y1998~ 63.43162961