JEE Main 2024 Mathematics question
If the solution curve y = y(x) of the differential equation (1 + y²)(1 + x)dx + x dy = 0, x > 0 passes through the point (1, 1) and then α + 2β is.
Answer: 3
Solution
Separating variables, ∫(1 + ln x)/x dx + ∫dy/(1 + y²) = 0, so (1 + ln x)²/2 + tan⁻¹y + C = 0. Passing through (1, 1): C = −1/2 − π/4.
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