AP EAMCET · Maths · Differential Equations
Solution of \(\frac{d y}{d x}=\frac{x \log x^2+x}{\sin y+y \cos y}\) is
- A \(y \sin y=x^2 \log x+C\)
- B \(y \sin y=x^2+C\)
- C \(y \sin y=x^2+\log x\)
- D \(y \sin y=x \log x+C\)
Answer & Solution
Correct Answer
(A) \(y \sin y=x^2 \log x+C\)
Step-by-step Solution
Detailed explanation
We have, \(\frac{d y}{d x}=\frac{x \log x^2+x}{\sin y+y \cos y}\) \(\Rightarrow(\sin y+y \cos y) d y=\left(x \log x^2+x\right) d x\) On integrating both sides, we get \(-\cos y+y \sin y+\cos y…
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