JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) satisfies the equation \(\frac{d y}{d x}-|A|=0\), for all \(x>0\), where \(A=\left[\begin{array}{ccc}y & \sin x & 1 \\ 0 & -1 & 1 \\ 2 & 0 & \frac{1}{x}\end{array}\right] .\) If \(y(\pi)=\pi+2\), then the value of \(y\left(\frac{\pi}{2}\right)\) is:
- A \(\frac{\pi}{2}-\frac{4}{\pi}\)
- B \(\frac{\pi}{2}-\frac{4}{\pi}\)
- C \(\frac{\pi}{2}-\frac{1}{\pi}\)
- D \(\frac{\pi}{2}+\frac{4}{\pi}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{2}+\frac{4}{\pi}\)
Step-by-step Solution
Detailed explanation
\(|\mathrm{A}|=\frac{-\mathrm{y}}{\mathrm{x}}+2 \sin x+2\) \(\frac{\mathrm{dy}}{\mathrm{dx}}=|\mathrm{A}|\) \(\frac{\mathrm{d} y}{\mathrm{~d} \mathrm{x}}=\frac{\mathrm{y}}{\mathrm{x}}+2 \sin \mathrm{x}+2\)…
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