上述方程基本是全微分方程：
(5y-2x)y'-2y=0,变形为：5ydy=2ydx+2xdy,故通解为：（5/2)y^2=2xy+C.
(e^x+y)dx+(2+x+ye^y)dy=0,变形为：e^xdx+ye^ydy+(ydx+xdy)+2dy=0
因为 ∫ye^ydy=∫yde^y=ye^y-e^y+c
所以：通解为：e^x+ye^y-e^y+xy+2y=C,将条件y(0)=1代入得：C=2+e
故特解为：e^x+ye^y-e^y+xy+2y=2+e