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)}…

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

[JEE Main 2023, 30 Jan (Shift 1)]