(x−y)y2p+(y−x)x2q=(x2+y2)z
(x−y)y2dx=(y−x)x2dy=(x2+y2)zdz
x2dx+y2dy=0
x3+y3=c1
(x−y)(x2+y2)dx−dy=(x2+y2)zdz
ln(x−y)=lnz+lnc2
zx−y=c2
F(c1,c2)=F(x3+y3,zx−y)=0
for the curve xz=a3,y=0 :
c1=x3
x/z=c2
⟹z=x/c2=3c1/c2
x/c2=a3/x⟹x2=c2a3
z=x−yz3x3+y3
3x3+y3=x−y
z=a3/x=a3/3c1=3x3+y3a3
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