化下列方程为齐次方程,并求出通解

题目

化下列方程为齐次方程,并求出通解
(x-y-1)dx+(4y+x-1)dy=0

答案

→dy/dx=-(x-y-1)/(4y+x-1)即dy/d(x-1)=-(-y+x-1)/(4y+x-1)令u=x-1,则dy/du=(y-u)/(4y+u)①令t=4y+u;则y=(1/4)(t-u).②则dy/du=(1/4)(dt/du-1)③将②③代入①得:(1/4)(dt/du-1)=(1/4)(t/u)-5/4.dt/du=t/u -4;④令v=t...