Step 1:
$y=3\cos(\log x)+4\sin(\log x)$
$\large\frac{dy}{dx}$$=y_1=3\sin(\log x).\frac{1}{x}$$+4\cos(\log x).\large\frac{1}{x}$
$xy_1=3\sin(\log x)+4\cos(\log x)$
Step 2:
Differentiating with respect to $x$ we get
$xy_2+y_1.1=\large\frac{3\cos(\log x)}{x}-\large\frac{4\sin(\log x)}{x}$
$xy_2+y_1=\large\frac{-1}{x}$$[3\cos (\log x)+4\sin(\log x)]$
$xy_2+y_1=\large\frac{-y}{x}$
$x^2y_2+xy_1=-y$
$x^2y_2+xy_1+y=0$