Let the solution curve {\y}= {\y}( {\x}) of the differential equation \frac{d y}{d x}- {3 x^5 \tan ^{-1} (x^3) }/{ (1+x^6) ^{\frac{3}{2}}} y=2 x \exp {x^3-\tan ^{-1} x^3}/{\sqrt{(1+x)^6}} pass through the origin. Then {\y} (1) is equal to : [30-Jan-2023 Shift 1]

Correct Answer is : exp(4−π4√2)

JEE Mains 30-Jan-2023 Shift 1 Solved Paper

Section: Mathematics

Question : 72 of 90

Marks: +1, -0

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

−‌

3x5tan−1(x3)

(1+x6)‌

y=2x
exp‌

x3−tan−1x3

√(1+x)6

pass through the origin.
Then y(1) is equal to :

[30-Jan-2023 Shift 1]

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