The question is
★
((x−y)y2)dx =((y−x)x2)dy = (x2+y2)dz
Consider these
((x−y)y2)dx =((y−x)x2)dy
We get
Integration of
∙
∫y2dy=∫−x2dx
∙
y3=−x3+c1
★
((x−y)y2)dx=(x2+y2)dz
⟹
∫y2dz=∫(x−y)(x2+y2)dx
⟹
∫(x−y)(x2+y2)dx =∫(x−y)+x+y)2y2dx =
2y2∫(x−y)1dx+∫xdx+y∫1dx=
= 2y2ln(x−y)+2x2+xy+c2
∙
★
y2ln(z)=2y2ln(x−y)+2x2+xy+c2
integral surface:
∙
y3=−x3+c1
∙
y2ln(z)=2y2ln(x−y)+2x2+xy+c2
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