∵(x²+y)dx+(x+y)dy=0 ==>x²dx+ydx+xdy+ydy=0
==>d(x³/3)+d(xy)+d(y²/2)=0
==>d(x³/3+xy+y²/2)=0
∴原方程的通解是x³/3+xy+y²/2=C (C是积分常数).
微分方程组(X^2+Y)dx+(x+y)dy=0的通解
∵(x²+y)dx+(x+y)dy=0 ==>x²dx+ydx+xdy+ydy=0
==>d(x³/3)+d(xy)+d(y²/2)=0
==>d(x³/3+xy+y²/2)=0
∴原方程的通解是x³/3+xy+y²/2=C (C是积分常数).