如题所述
解:微分方程为y'+1/xy=1/x,化为xyy'+1=y,xy'=(y-1)/y,ydy/(y-1)=dx/x,[1+1/(y-1)]dy=dx/x,y+ln|y-1|=ln|x|+ln|c|(c为任意非零常数),方程的通解为(y-1)e^y=cx
微分方程为y'+1/x·y=1/x,化为xy'+y=1,
(xy)'=1,xy=x+c(c为任意常数),方程的通解为y=(x+c)/x