CUET · MATHS · PYQ PAPER 2023
If \(y=3 \cos (\log x)+4 \sin (\log x)\), then choose correct option :
- A \(x^2 y^{\prime \prime}-x y^{\prime}+y=0\)
- B \(x^2 y^{\prime \prime}+x y^{\prime}-y=0\)
- C \(x^2 y^{\prime \prime}+x y^{\prime}+y=0\)
- D \(x^2 y^{\prime \prime}-x y^{\prime}-y=0\)
Answer & Solution
Correct Answer
(C) \(x^2 y^{\prime \prime}+x y^{\prime}+y=0\)
Step-by-step Solution
Detailed explanation
\(y = 3 \cos (\log x) + 4 \sin (\log x)\) \(y' = -3 \sin (\log x) \cdot \frac{1}{x} + 4 \cos (\log x) \cdot \frac{1}{x}\) \(x y' = -3 \sin (\log x) + 4 \cos (\log x)\) \(1 \cdot y' + x y'' = -3 \cos (\log x) \cdot \frac{1}{x} - 4 \sin (\log x) \cdot \frac{1}{x}\)…
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