Given integral equation (2x2+6xy−y2)dx+(3x2−2xy+y2)dy=0
Group the given terms as follow,
2x2dx+y2dy−(y2dx+2xydy)+3x2dy+6xydx=02x2dx+y2dy−d(xy2)+3d(x2y)=0
Integrating, we get
∫2x2dx+∫y2dy−∫d(xy2)+∫3d(x2y)=0
2x33+y33−xy2+3x2y=C∴2x3+y3−3xy2+9x2y=C′ Where C′=3C