AP EAMCET · Maths · Differential Equations
If \(y=x \log \left(\frac{1}{a x}+\frac{1}{a}\right)\), then \(x(x+1) \frac{d^2 y}{d x^2}+x \frac{d y}{d x}-y=\)
- A 0
- B \(1+x\)
- C \(-1\)
- D \(\mathrm{x}\)
Answer & Solution
Correct Answer
(C) \(-1\)
Step-by-step Solution
Detailed explanation
\(y=x \log \left(\frac{1}{a x}+\frac{1}{a}\right)\) Then \(\frac{d y}{d x}=x \cdot \frac{1}{\left(\frac{1}{a x}+\frac{1}{a}\right)} \cdot\left(-\frac{a}{a x^2}\right)+\log \left(\frac{1}{a x}+\frac{1}{a}\right)\)…
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