Question

Let \(y=\frac{1}{1+x+\ln x}\), Then
(A) \(x \frac{d y}{d x}+y=x\)
(B) \(x \frac{d y}{d x}=y(y \ln x-1)\)
(C) \(x^{2} \frac{d y}{d x}=y^{2}+1-x^{2}\)
(D) \(x\left(\frac{d y}{d x}\right)^{2}=y-x\)

Answer 1

Ans : (B)
Hint : \(x \frac{d y}{d x}=y(y \ln x-1)\)