JEE Math Practice Question
Let $$y=y(x)$$ be the solution curve of the differential equation $$ \frac{d y}{d x}+\frac{1}{x^{2}-1} y=\left(\frac{x-1}{x+1}\right)^{1 / 2}$$, $$x >1$$ passing through the point $$\left(2, \sqrt{\frac{1}{3}}\right)$$. Then $$\sqrt{7}\, y(8)$$ is equal to :
- A.$$11+6 \log _{e} 3$$
- B.19
- C.$$12-2 \log _{\mathrm{e}} 3$$
- D.$$19-6 \log _{\mathrm{e}} 3$$
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