If `ysqrt(x^2+1)=log(sqrt(x^2+)1-x),s howt h a t(x^2+1)(dy)/(dx)+x y+1=0`

Explanation

$$ \sqrt{x^{2}+1}=\log \left\{\sqrt{x^{2}+1}-x\right\} $$
Differentiating with reset to be `x` we get
$$
\begin{aligned}
&\sqrt{x^{2}+1} \frac{d y}{d x}+\frac{1}{2 \sqrt{x^{2}+1}} \cdot 2 x \cdot y=\frac{1}{\sqrt{x^{2}+1}-x}\left\{\frac{1}{2 \sqrt{x^{2}+1}} 2 x-1\right\} \\
&\sqrt{x^{2}} \frac{d y}{d x}+\frac{x y}{\sqrt{x^{2}+1}}=\frac{1}{\sqrt{x^{2}+1-x}}\left\{\frac{x}{\sqrt{x^{2}+1}-1}\right\} \\
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