18復丂堿娭悢

丂丂Maple丂傪梡偄偰丄 x²-xy+y²-3=0偱掕傑傞堿娭悢丂y=φ(x)偺僌儔僼傪昤偄偰傒傑偟傚偆丅

亜solve丂(x²-x*y+y²-3=0,丂y丂)丂

偲偡傞丂(x²-xy+y²-3 = 0傪 y 偵偮偄偰夝偔 ) 偲丄 x²-xy+y²-3 = 0偱掕傑傞堿娭悢偑媮傑傝傑偡丅 2師曽掱幃偵懳偡傞夝偺岞幃傪梡偄偰庤寁嶼傪峴偭偰傕媮傔傜傟傑偡丅

偙傟傜偺僌儔僼傪掕媊堟丂[-2,2]丂偱昤偒傑偡丅

亜plot({1/2*x+1/2*sqrt(-3*x^2+12),1/2*x-1/2*sqrt(-3*x^2+12)}丂,丂x=-2丂.丂.丂2丂)丂

幚廗18.1 丂x³+3x²-y²丂=丂0丂偱掕傑傞堿娭悢偺僌儔僼傪昤偄偰傒傑偟傚偆丅

[惓夝椺]

Maple丂偵偼丄implicitplot丂偲偄偆娭悢偑梡堄偝傟偰偍傝丄偙傟傪梡偄傞偲娙扨偵昞帵偡傞偙偲偑偱偒傑偡丅

亜丂with丂(plots):
亜丂implicitplot丂(丂x^2-x*y+y^2-3=丂0丂,丂丂x=-2丂.丂.丂2丂,丂y=-2丂.丂.丂2丂)丂

嬋慄傪側傔傜偐偵昞帵偟偨偄偲偒偵偼丄numpoints=10000側偳偲僆僾僔儑儞傪偮偗傞偲傛偄偱偡丅

幚廗丂18.2 丂x³+3x²-y²丂=丂-1丂,x³+3x²-y² 丂=丂0丂,x³+3x²-y²丂=丂1丂 偱掕傑傞堿娭悢偺僌儔僼傪偦傟偧傟昤偄偰傒傑偟傚偆丅傑偨丄 z=x³+3x²-y² 偺僌儔僼傪摍崅慄傪昞帵偝偣偰昤偄偰斾妑偟偰傒傑偟傚偆丅

[惓夝椺]

幚廗丂18.3 丂嬋慄丂x³-3xy+y³丂=丂0丂傪丂xy丂暯柺忋偵恾帵偟偰傒傑偟傚偆丅傑偨丄z=x³-3xy+y³丂偺僌儔僼傪摍崅慄傪昞帵偝偣偰昤偄偰斾妑偟偰傒傑偟傚偆丅

[惓夝椺]

f(x,y)=0 偱掕傑傞堿娭悢y=冇(x)偺摫娭悢y'=冇(x)傪媮傔傞偵偼丄implicitdiff僐儅儞僪傪梡偄傑偡丅

>implicitdiff(f(x,y)=0,y,x)丂丂
(f(x,y)=0偱掕傑傞堿娭悢y傪x偱旝暘)

>implicitdiff(f(x,y)=0,y,x,x)丂
(f(x,y)=0偱掕傑傞堿娭悢y傪x偱擇夞旝暘

幚廗18.4丂f(x,y)偑C2媺偺偲偒丄f(x,y)=0偱掕傑傞堿娭悢y=冇(x)偵懳偟丄師偑惉傝棫偮偙偲傪妋偐傔側偝偄丅
丂丂丂y'=冇'(x)=-f_x/f_y
丂丂丂y''=冇''(x)=-(f_xx f_y²-2f_xy f_x f_y+f_yy f_x²)/ f_y³

[惓夝椺]