1、y’=(xy+y)/(x+xy),y(1)=1 2、(y/x)y’+e^y=0,y(1)=0 求解微分方程,

1、y’=(xy+y)/(x+xy),y(1)=1 2、(y/x)y’+e^y=0,y(1)=0 求解微分方程,
1、y’=(xy+y)/(x+xy),y(1)=1 2、(y/x)y’+e^y=0,y(1)=0 求解微分方程,

1、y’=(xy+y)/(x+xy),y(1)=1 2、(y/x)y’+e^y=0,y(1)=0 求解微分方程,
1.dy/dx=y(x+1)/[x(y+1)]
(y+1)/ydy=(x+1)/xdx
两边积分：∫(1+1/y)dy=∫(1+1/x)dx
y+ln|y|=x+ln|x|+C
令x=1：C=0
所以y+ln|y|=x+ln|x|
2.y/x*dy/dx=-e^y
ye^(-y)dy=-xdx
两边积分,
左边=-∫yd(e^(-y))=-ye^(-y)+∫e^(-y)dy=-ye^(-y)-e^(-y)+C
右边=-x^2/2+C
即e^(-y)(y+1)=x^2/2+C
令x=1：1=1/2+C,C=1/2
所以e^(-y)(y+1)=(x^2+1)/2