If y = y(x), x (0, /2) be the solution curved of the differential equation ( ^ 2 2x)dy/dx + (8 ^ 2 2x + 2 4x)y = 2e^ -4x (2 2x + 2x), with y( /4) = e^ - , then y( /6) is equal to -

JEE Main 2022 Mathematics question

If y = y(x), x (0, ) be the solution curved of the differential equation , with , then is equal to -

Answer: (A)

Dividing by , dy/dx + (8 + 4cot sin 2x + cos . The integrating factor is + 4cot2x)dx} = . So y sin 2x + cos 2x)dx = sin 2x + C (since

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Question ID VK-034785