已知y=x/lnx是微分方程y'=y/x+φ(x/y)的解,则φ(x/y)的表达式是?A.-(y^2)/(x^2)B.(y^2)/(x^2)C.-(x^2)/(y^2)D.(x^2)/(y^2)
网友回答
你直接代进去不就是了吗..
y'=(lnx-1)/(lnx)^2
φ(x/y)=y'-y/x=(lnx-1)/(lnx)^2-1/lnx
=-1/(lnx)^2=-y^2/x^2
A======以下答案可供参考======
供参考答案1:
y = x/lnx
y' = (lnx - 1)/(lnx)^2
y'=y/x+φ(x/y)
(lnx - 1)/(lnx)^2 = (x/lnx)/x = φ(x/y)
φ(x/y) = (lnx - 1)/(lnx)^2 - 1/lnx
= -1/(lnx)^2
= -y^2/x^2