一类可化为变量分离微分方程的题型推广

The promotion of a kind of transformable separation of variables differential equations

对一类可化为变量分离方程的微分方程dy/dx=(a1x+b1y+c1)/(a2x+b2y+c2)(a1,a2,b1,b2,c1,c2均为常数)进行了次数上的推广,得到方程dy/dx=(a1xα+b1xβyγ+cxβ)/(a1yα+b1xγyβ-cyβ)(β+γ=α,β=γ-1),并给出其通用解法.

Promoted the index number of the transformable separation of variables differential equations dy/dx=a1x＋b1y＋c1/a2x＋b2y＋c2b2（a1,a2,b1,b2,c1,c2 are constant ）, obatained the differential equations dy/dx=a1xα＋b1xβyγ＋cxβ/a1yα＋b1xγyβ＋cyβ（β＋γ=α,β=γ-1）,and the general solution was given.