Question

求微分方程y'+y/x=1/x的通解

Answer 1

通解y=1+cx
解法：dy/dx=(1-y)/x
dy/(1-y)=dx/x
-ln(1-y)=lnx+c1
1-y=e^-(1nx+c1)
1-y=-e^c1*x
1-y=-cx
y=1+cx (c为const）