∵(x+2y)dx+(2x-3y)dy=0 ==>xdx+2ydx+2xdy-3ydy=0
==>xdx+2(ydx+xdy)-3ydy=0
==>d(x²)/2+2d(xy)-3d(y²)/2=0
==>x²/2+2xy-3y²/2=C/2 (C是积分常数)
==>x²+4xy-3y²=C
∴原微分方程的通解是x²+4xy-3y²=C (C是积分常数)