CUET · MATHS · PYQ PAPER 2023
Solution of \(\frac{dy}{dx} = 2^{y-x}\) is:
- A \(2^{-y}+2^{-x}=k\)
- B \(2^{-y}=k-3 \cdot 2^{-x}\)
- C \(2^{-y}-2^{-x}=k\)
- D \(2^{-y}-5 \cdot 2^{-x}=k\)
Answer & Solution
Correct Answer
(C) \(2^{-y}-2^{-x}=k\)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{2^y} = 2^{-x} dx\) \(\int 2^{-y} dy = \int 2^{-x} dx\) \(-\frac{2^{-y}}{\ln 2} = -\frac{2^{-x}}{\ln 2} + C\) \(2^{-y} = 2^{-x} - C \ln 2\) \(2^{-y} - 2^{-x} = k\)
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