微分方程x*dy/dx+y=3

题目

微分方程x*dy/dx+y=3
它的通解是Y=C/x+3吗,我把通解带进去求等是不相等,
xdy + (y-3)dx = 0
到xd(y-3) + (y-3)dx = 0不懂，xd(y-3) 怎么变过去的呢

答案

x*dy/dx+y=3两边同时乘以dxxdy + (y-3)dx = 0soxd(y-3) + (y-3)dx = 0sod[x(y-3)] = 0sox(y-3)=C C is a constantsoy=C/x+3检验：x*dy/dx+y=x*(-C/x^2) + C/x+3 = -C/x + C/x+3 = 3,满足原方程.