JEE Mains · Maths · STD 12 - 9. differential equations
If \(\frac{d y}{d x}+\frac{2^{x-y}\left(2^{y}-1\right)}{2^{x}-1}=0, x, y>0, y(1)=1\), then \(y (2)\) is equal to
- A \(2+\log _{2} 3\)
- B \(2+\log _{2} 2\)
- C \(2-\log _{2} 3\)
- D \(2-\log _{2} 3\)
Answer & Solution
Correct Answer
(D) \(2-\log _{2} 3\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}+\frac{2^{x-y}\left(2^{y}-1\right)}{2^{x}-1}=0,\) \(x , y >0, y (1)=1, y (2)=?\) \(\frac{d y}{d x}=-\frac{2^{x}\left(2^{y}-1\right)}{2^{y}\left(2^{x}-1\right)}\) \(\int \frac{2^{y}}{2^{y}-1} d y=-\int \frac{2^{x}}{2^{x}-1} d x\)…
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