AP EAMCET · Maths · Differential Equations
If \(\lim _{x \rightarrow \infty} y(x)=\frac{\pi}{2}\), then the solution of \(x^3 \sin y \frac{d y}{d x}=2\) is \(\cos y=\)
- A \(\frac{3}{\mathrm{x}^2}\)
- B \(\frac{1}{x}\)
- C \(\frac{1}{x^2}\)
- D \(\frac{2}{x^3}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{x^2}\)
Step-by-step Solution
Detailed explanation
\(\because \quad x^3 \sin y \frac{d y}{d x}=2 \Rightarrow \sin y d y=\frac{2}{x^3} d x\) Integrating both sides, we get \(\int \sin y d y=2 \int \frac{1}{x^3} d x \Rightarrow-\cos y=2 \cdot \frac{x^{-2}}{-2}+C\) \(\Rightarrow \quad \cos y=\frac{1}{x^2}-C\) ...(i) Taking…
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