What is the solution for x(xz)+(xz)^2dx-x^2(xdz+zdx)=0 ?

The solution for x(xz)+(xz)^2dx-x^2(xdz+zdx)=0 is z=-1/(ln(x)+c_{1)}

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x(xz)+(xz)^2dx-x^2(xdz+zdx)=0

x (x z) + (x z)^{2} d x - x^{2} (x d z + z d x) = 0

z = - \frac{1}{ln ( x ) + c _{1}}

Solution steps

x (x z) + (x z)^{2} d x - x^{2} (x d z + z d x) = 0

Solve separable ODE:

z = - \frac{1}{ln ( x ) + c _{1}}

z = - \frac{1}{ln ( x ) + c _{1}}

What is the solution for x(xz)+(xz)^2dx-x^2(xdz+zdx)=0 ?
The solution for x(xz)+(xz)^2dx-x^2(xdz+zdx)=0 is z=-1/(ln(x)+c_{1)}