JEE Main 2024 Mathematics question
If the solution of the differential equation (2x + 3y – 2)dx + (4x + 6y – 7)dy = 0, y(0) = 3, is αx + βy + |2x + 3y – γ| = 6, then α + 2β + 3γ is equal to .
Answer: 29
Solution
Put t = 2x + 3y: dt/dx = 2 + 3 dy/dx, which gives ∫(2t − 7)/(t − 8) dt = ∫dx, i.e. 2t + 9 ln|t − 8| = x + c. With y(0) = 3 (t =
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