<s>[INST] the total differential equation $(y^2z - y^3 +x^2y)dx - (x^2z +x^3 -xy^2)dy +(x^2y - xy^2)dz=0$ In solving the total differential equation $$(y^2z - y^3 +x^2y)dx - (x^2z +x^3 -xy^2)dy +(x^2y - xy^2)dz=0$$
Substituting $x =uz$ and $y=vz$ and reached at a position where, i face the following
$$(v^2 - v^3 +u^2v)du - (u^2+u^3-uv^2)dv=0$$
I am stuck here please help!!
 [/INST] It's all equation devided by x^2 y^2.
Now we  get
(z-y/x^2 +1/y)dx-(z+x/y^2 - 1/x)dy+(1/y-1/x)dz
d(x/y) +d(y/x) +z(dx-dy) +(1/y-1/x)dz
d(x/y) +d(y/x) +d(z/y) - d(z/x) = 0
x+y + log y - log x = c
x+y+ log  y/ x = c
x + y + log y / x = c. 
Is a required solution. 
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