If `y=3cos(logx)+4sin(logx),\ ` then show that `x^2(d^2\ y)/(dx^2)+x(dy)/(dx)+y=0`

Explanation

To show that \( x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} + y = 0 \) for \( y = 3 \cos(\log x) + 4 \sin(\log x) \), we will follow these steps:

### Step 1: Find the first derivative \( \frac{dy}{dx} \)

Given:
\[ y = 3 \cos(\log x) + 4 \sin(\log x) \]
...