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If y=3cos(logx)+4sin(logx),show that x^...

If `y=3cos(logx)+4sin(logx),`show that `x^2y_2+x y_1+y=0`.

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To show that \( x^2 y_2 + x y_1 + y = 0 \) for the function \( y = 3 \cos(\log x) + 4 \sin(\log x) \), we will first find the first derivative \( y_1 \) and the second derivative \( y_2 \) of \( y \) with respect to \( x \). ### Step 1: Find the first derivative \( y_1 \) Given: \[ y = 3 \cos(\log x) + 4 \sin(\log x) \] ...
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