Question

Let the solution curve $y=y(x)$ of the differential equation \frac{d y}{d x}-\frac{3 x^5 \tan ^{-1}\left(x^3\right)}{\left(1+x^6\right)^{3 / 2}} y=2 x \exp \left\\{\frac{x^3-\tan ^{-1} x^3}{\sqrt{\left(1+x^6\right)}}\right\\} pass through the origin Then $y(1)$ is equal to :

• A. $\exp \left(\frac{4+\pi}{4 \sqrt{2}}\right)$
• B. $\exp \left(\frac{4-\pi}{4 \sqrt{2}}\right)$
• C. $\exp \left(\frac{1-\pi}{4 \sqrt{2}}\right)$
• D. $\exp \left(\frac{\pi-4}{4 \sqrt{2}}\right)$

Answer 1

Answer: (B)

$\exp \left(\frac{4-\pi}{4 \sqrt{2}}\right)$

Answer 2

The correct option is (B) : $\exp \left(\frac{4-\pi}{4 \sqrt{2}}\right)$