Question

高等数学微分方程

如图，这题的微分方程是怎么求出来的，求下过程，谢谢啦哈

Answer 1

d(yy')=dy，两边积分就得到yy' = y+C,
yy'=y+c
ydy/(y+c)=dx
[1-1/(y+c)]dy=dx
两边再积分得到
y - ln|y+c|=x +c'

Answer 2

d(yy') = dy, yy' = y+C1
y ≠ 0 时， y' = dy/dx = (y+C1)/y
ydy/(y+C1) = dx, (y+C1-C1)dy/(y+C1) ,
[1-C1/(y+C1)]dy = dx, y - C1ln|y+C1| = x + C2