If the solution of the differential equation (2 x+3 y-2) \dx+(4 x+6 y-7) d y=0, y(0)=3, is \alpha x+\beta y+3 \log _e 2 x+3 y-\gamma|=6, then \alpha+2 \beta+3 \gamma is equal to____ [27-Jan-2024 Shift 1]

JEE Main 27-Jan-2024 Shift 1 Solved Paper

Section: Mathematics

Question : 23 of 90

Marks: +1, -0

If the solution of the differential equation (2x+3y−2)‌dx+(4x+6y−7)dy=0,y(0)=3, is αx+βy+3loge2x+3y−γ|=6, then α+2β+3γ is equal to____

[27-Jan-2024 Shift 1]

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