AP EAMCET · Maths · Differential Equations
If \(y=y(x)\) is the solution of \(\frac{d y}{d x}=\frac{x-y \cos x}{1+\sin x}, y\left(\frac{\pi}{2}\right)=\frac{\pi^2}{8}\), then \(y(\pi)=\)
- A \(\frac{5 \pi^2}{8}\)
- B \(\frac{7 \pi^2}{8}\)
- C \(\frac{9 \pi^2}{8}\)
- D \(\frac{12 \pi^2}{7}\)
Answer & Solution
Correct Answer
(A) \(\frac{5 \pi^2}{8}\)
Step-by-step Solution
Detailed explanation
\(\because \frac{d y}{d x}=\frac{x-y \cos x}{1+\sin x}\) \(\Rightarrow \frac{d y}{d x}=\frac{x}{1+\sin x}-y \frac{\cos x}{1+\sin x}\) \(\Rightarrow \frac{d y}{d x}+\frac{\cos x}{1+\sin x} y=\frac{x}{1+\sin x}\) ...(i) Eqn. (i) is a linear differential equation of first order and…
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