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Mathematics Question on Differential equations

For solution of differential equation
dydx−3x5tan⁡−1(x3)(1+x6)32y=x3tan⁡−1x31+x6\frac{dy}{dx}-\frac{3x^5\tan^{-1}(x^3)}{(1+x^6)^{\frac{3}{2}}}y=\frac{x^3\tan^{-1}x^3}{\sqrt{1+x^6}}
given that y(0) = 0 then y(1) is

A

1−eπ421-e^{\frac{\pi}{4\sqrt2}}

B

1−e(12−π42)1-e^{(\frac{1}{\sqrt2}-\frac{\pi}{4\sqrt2})}

C

e12−eπ42e^{\frac{1}{\sqrt2}}-e^{\frac{\pi}{4\sqrt2}}

D

eπ42e^{\frac{\pi}{4\sqrt2}}

Answer

1−e(12−π42)1-e^{(\frac{1}{\sqrt2}-\frac{\pi}{4\sqrt2})}

Explanation

Solution

The correct answer is (B) : 1−e(12−π42)1-e^{(\frac{1}{\sqrt2}-\frac{\pi}{4\sqrt2})}