Answer to Question #128393 in Differential Equations for Nisha

Question

Solve y^2dx-z dy+dz=0 equation for
Exact differential equation Method

Answer 1

$y^2dx-zdy+dz=Pdx+Qdy+Rdz=0\Rightarrow\quad \\ P=y^2,\quad Q=-z,\quad R=1\Rightarrow\\ \Delta=P(Q'_z-R'_y)+Q(R'_x-P'_z)+R(P'_y-Q'_x)=\\ =y^2(-1-0)-z(0-0)+1\cdot (2y-0)=-y^2+2y\neq0\Rightarrow\\ this \quad equation\quad is\quad non\quad integrable;$