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

Question

Let the solution curve $y=y(x)$ of the differential equation

$$ \frac{\mathrm{d} y}{\mathrm{~d} x}-\frac{3 x^{5} \tan ^{-1}\left(x^{3}\right)}{\left(1+x^{6}\right)^{3 / 2}} y=2 x \exp \left\{\frac{x^{3}-\tan ^{-1} x^{3}}{\sqrt{\left(1+x^{6}\right)}}\right\} \text { pass through the origin. Then } y(1) \text { is equal to : } $$

$\exp \left(\frac{1-\pi}{4 \sqrt{2}}\right)$

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

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

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

Solution

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