A homogeneous differential equation of the from `(dx)/(dy)=h(x/y)`can be solved by making the substitution.(A) `y = v x` (B) `v = y x` (C) `x = v y` (D) `x = v`

Explanation

To solve the problem of identifying the correct substitution for a homogeneous differential equation of the form \(\frac{dx}{dy} = h\left(\frac{x}{y}\right)\), we will analyze the given options step by step.

### Step-by-Step Solution:

1. **Understanding the Homogeneous Equation**:
A homogeneous differential equation can be expressed in the form \(\frac{dx}{dy} = h\left(\frac{x}{y}\right)\). This means that the function \(h\) depends on the ratio \(\frac{x}{y}\).

2. **Evaluating Option A: \(y = vx\)**:
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