Question

微分方程求通解

(x-2y+5)dx+(2x-y+4)dy=0求通解，求大神们告知求解过程撒

Answer 1

Answer 2

设u=x+1,v=y-2代入得：
(u-2v)du+(2u-v)dv=0
du/dv=(v-2u)/(u-2v)= (1-2u/v)/(u/v-2)
设u/v=z u=vz ,du/dv=z+vdz/dv
z+vdz/dv= (1-2z)/(z-2)
vdz/dv= (1-2z)/(z-2)-z=(1-z^2)/(z-2)
(z-2)dz/(1-z^2)=dv/v
(-1/2)ln(1-z^2)-2ln(1-z)/(1+z)=lnv+lnC
剩下就是化简和代回原变量，自己做吧。
下班啦

Answer 3