Let $ y=y(x) $ satisfies the equation $ \frac{d y}{d x}-|A|=0 $, for all $ x0 $, 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: [JEE Main 2021, 20 Jul (Shift 2)]

Question

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: [JEE Main 2021, 20 Jul (Shift 2)]

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Let \( y=y(x) \) satisfies the equation \( \frac{d y}{d x}-|A|=0 \), for all \( x>0 \), where \( A=\left[\begin{array…

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Let \( y=y(x) \) satisfies the equation \( \frac{d y}{d x}-|A|=0 \), for all \( x&gt;0 \), where \( A=\left[\begin{array…

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Let \( y=y(x) \) satisfies the equation \( \frac{d y}{d x}-|A|=0 \), for all \( x>0 \), where \( A=\left[\begin{array…