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AP EAMCET · Maths · Differential Equations

If \(\log y\) is an integrating factor of \(\frac{d x}{d y}+P(y) x=Q(y)\), then \(\mathrm{P}(\mathrm{y})=\)

  1. A \(\frac{1}{y+\log y}\)
  2. B \(\frac{y}{\log y}\)
  3. C \(\frac{\log y}{y}\)
  4. D \(\frac{1}{y \log y}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{1}{y \log y}\)

Step-by-step Solution

Detailed explanation

I. \(F=\log y\) \(\begin{aligned} & \Rightarrow e^{\int P(y) d y}=\log y \\ & \Rightarrow \quad \int P(y) d y=\log (\log y)\end{aligned}\) Differentiating both sides, we get…