Promoted the index number of the transformable separation of variables differential equations d y d x=a x b y c a x b y c 1+ +αβ γ1 1 d d a x b x y cx y++β+ + ( 1a , 2a , 1b , 2b , 1c , 2c are constant),obatained the differential equations=1 1αγ ββ2 2 2 x a y b x y cy 1+1−(β γ α β γ+ = = − ,and the general solution was given. , 1)% 对一类可化为变量分离方程的微分方程(a1, a2, b1, b2, c1, c2均为常数)进行了次数上的推广,得到方程1111 d (,1) d y a x b x y cx x a y b x y cy αβγβαγβββγαβγ++=+==−+−,并给出其通用解法。
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