Let the solution curve y=y(x) of the differential equation dydx-3x5tan-1x31+x632y=2x expx3-tan-1x3(1+x)6 pass through the origin. Then y(1) is equal to:

Question

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

\exp (\frac{4 - π}{4 \sqrt{2}})

\exp (\frac{π - 4}{4 \sqrt{2}})

\exp (\frac{1 - π}{4 \sqrt{2}})

\exp (\frac{4 + π}{4 \sqrt{2}})

Solution

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