Question

[y+(x^2)y]dy=[x(y^2)-x]dx ,dy=x(e^x)(1+y^2)dx 这两题的通解

Answer 1

1、分离变量y/(y^2-1)dy＝x/(x^2+1)dx,两边积分1/2ln(y^2-1)=1/2ln(x^2+1)+1/2lnC,所以通解是y^2-1=C(x^2+1)

2、分离变量dy/(y^2+1)=xe^xdx,两边积分：arctany=(x-1)e^x+C