>>835
(左辺) = 2(1+x)(xdy-ydx) - (1+3x)dy + (1-x+y)dx
= (2x+1){ (x-1)dy + [-y -(x-1)/(2x+1)]dx }
= (2x+1)(x-1)^2 { dy/(x-1) + [-y/(x-1)^2 +(1/3)[2/(2x+1) -1/(x-1)]dx }
= (2x+1)(x-1)^2 d{ y/(x-1) + (1/3)log|(2x+1)/(x-1)| }.

これが =0 ならば { y/(x-1) + (1/3)log|(2x+1)/(x-1)| } = c.

おやすみ