Let y = y(x) be the solution curve of the differential equation (2x^ 2 ) _ e ( x^ 2 )dy + (4xy - 4 2 x (x^ 2 - /4))dx = 0, 0 < x < /2 , which passes through the point ( /6 , 1). Then |y( /3 )| is equal to _____ .

JEE Main 2022 Mathematics question

Let y = y(x) be the solution curve of the differential equation x , , which passes through the point (, 1). Then is equal to .

Answer: 1

Divide by ln(tan ) dx: dy/dx + ln(tan x ln(tan )). The integrating factor is dx/(sin ln tan ). With , y ln(tan \int\sqrt{2}$

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Question ID VK-034440