If `y=x/(log|cx|)` (where `c` is an arbitrary constant) is the general solution of the differential equation `(dy)/(dx)=y/x+varphi(x/y),` then the function `varphi(x/y)` is

Options

A. `x^(2)//y^(2)`
B. `-x^(2)//y^(2)`
C. `y^(2)//x^(2)`
D. `-y^(2)//x^(2)`

Explanation

To solve the problem, we need to find the function \(\varphi(x/y)\) given that \(y = \frac{x}{\log|cx|}\) is the general solution of the differential equation:

\[ \frac{dy}{dx} = \frac{y}{x} + \varphi\left(\frac{x}{y}\right) \]

### Step 1: Differentiate \(y\) with respect to \(x\)

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