Question

求x(1+y平方)dx-y(1+x平方)dy=0的通解有过程!

Answer 1

x(1+y平方)dx-y(1+x平方)dy=0

x(1+y平方)dx=y(1+x平方)dy

y/(1+y²)dy=x/(1+x²)dx

2y/(1+y²)dy=2x/(1+x²)dx

1/(1+y²)d(1+y²)=1/(1+x²)d(1+x²)

两边同时积分得

ln((1+y²))=ln(1+x²)+lnc

(1+y²)=c(1+x²)