求微分方程的通解：nxdy/dx+2y=xy^n+1

Question

求微分方程的通解：nx dy/dx + 2y = xy^n+1

Answer 1

nxy' + 2y = xy^(n+1)
ny'/y^(n+1) + 2y/y^(n+1)x =1
令y^(-n)=z (-n)y^(-n-1)y'=z' 代入：
z'-(2/x)z=1
通解y^(-n)=z=Cx^2-x