AP EAMCET · Maths · Differential Equations
If \(x \log x \frac{d y}{d x}+y=\log x^2\) and \(y(e)=0\), then \(y\left(e^2\right)=\)
- A \(0\)
- B \(1\)
- C \(\frac{1}{2}\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{dx} + \frac{1}{x \log x} y = \frac{2}{x}\) I.F. \( = e^{\int \frac{1}{x \log x} dx} = \log x\) \(y \log x = \int \frac{2 \log x}{x} dx = (\log x)^2 + C\) \(y(e)=0 \implies 0 = (\log e)^2 + C \implies C = -1\)…
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