If the solution curve y=y(x) of the differential equation (1+y^2) (1+\log _e x) \dx+x d y=0, x>0 passes through the point (1,1) and y(e)=\binom{\alpha-\tan (\frac{3}{2}) }/{\beta+\tan (\frac{3}{2}) }, then \alpha+2 \beta is [29-Jan-2024 Shift 1]

JEE Main 29-Jan-2024 Shift 1 Solved Paper

Section: Mathematics

Question : 26 of 90

Marks: +1, -0

If the solution curve y=y(x) of the differential equation (1+y2)(1+logex)‌dx+xdy=0,x>0 passes through the point (1,1) and y(e)=‌

α−tan(

)

β+tan(‌

)

, then α+2β is

[29-Jan-2024 Shift 1]

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