integral curve of dx/y^2+yz+x^2= dy/y^2-xz+x^2=dz/z(x+y)
We first subtract the first expression from the second and equate to the third expression
Simplify to get
d(x-y)=1dz
Integrate both sides
x-y+C=z
z=x-y+C1 ,this is the first integral curve
Second we add the third expression to the second and then equate with the first expression
Simplify to get
Further simply by multiplying both sides with y2+yz+x2 to get
dx=dy+dz=d(y+z)
Integrate both sides
x+C2=y+z
z=x-y+C2
Thus the equation only has one integral curve: z=x-y+C
Which can also be written, z-x+y=C
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