y''=(y')³+y'，令p=y'=dy/dx，则y''=dp/dx=(dp/dy)(dy/dx)=pp'pp'=p³+pp=0或p'=p²+1y=C或dp/(p²+1)=dyarctanp=y+C，dy/dx=p=tan(y+C)dy/tan(y+C)=dxlnsin(y+C)=x+Csin(y+C1)=C2e^x
