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JEE Main 2024 Mathematics question

MathematicsDifferential EquationJEE Main 2024

Let y = y(x) be the solution of the differential equation (x + y + 2)² dx = dy, y(0) = −2. Let the maximum and minimum values of the function y = y(x) in be α and β, respectively. If (3α + π)² + β² = γ + δ, γ, δ ∈ Z, then γ + δ equals …..

Answer: 31

Solution

With u = x + y + 2, du/dx = 1 + u², so u = tan x and y = tan x − x − 2 (increasing). Then β =

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Question ID VK-011397