Answer to Question #254766 in Differential Equations for Zode

Question

xy^2dx+zx^2dy-x^2y^2dz= determine the following equation are integral

Answer 1

$xy^{\mathrm{2}}\ dx\ +\ \ zx^{\mathrm{2}}\ dy\ \ \ -\ \ x^{\mathrm{2}}y^{\mathrm{2}}\ dz\ =0 \\ \frac{y^{\mathrm{2}}d\left(x^{\mathrm{2}}\right)}{\mathrm{2}}\ \ +\ zx^{\mathrm{2}}\ dy-\ x^{\mathrm{2}}y^{\mathrm{2}}\ dz\ =0 \\ \\ \int{\left(\frac{y^{\mathrm{2}}d\left(x^{\mathrm{2}}\right)}{\mathrm{2}}\right)}{}{}+\ \ \int{zx^{\mathrm{2}}dy{}{}{}{}\ \ -\ \ \ \int{\left(x^{\mathrm{2}}y^{\mathrm{2}}\ dz\ \right)=0}} \\ \\ \frac{\left(x^{\mathrm{2}}y^{\mathrm{2}}\right)}{\mathrm{2}}+yzx^{\mathrm{2}}{}-{}{}x^{\mathrm{2}}y^{\mathrm{2}}\ z{}{}{}\ \ =\ \ C$