JEE Mains · Maths · STD 12 - 9. differential equations
If the solution of the differential equation \((2 x+3 y-2) d x+(4 x+6 y-7) d y=0, y(0)=3\), is \(\alpha x+\beta y+3 \log _e|2 x+3 y-\gamma|=6\), then \(\alpha+2 \beta+3 \gamma\) is equal to
- A \(85\)
- B \(25\)
- C \(29\)
- D \(42\)
Answer & Solution
Correct Answer
(C) \(29\)
Step-by-step Solution
Detailed explanation
\( 2 x+3 y-2=t \quad 4 x+6 y-4=2 t \) \( 2+3 \frac{d y}{d x}=\frac{d t}{d x} \) \( \frac{d y}{d x}=\frac{-(2 x+3 y-2)}{4 x+6 y-7} \) \( \frac{d t}{d x}=\frac{-3 t+4 t-6}{2 t-3}=\frac{t-6}{2 t-3} \) \( \int \frac{2 t-3}{t-6} d t=\int d x \)…
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