Order of the differential equation whose general solution is `y = (ax)/(bx + c)`, where a, b, c are arbitrary constants is

Options

A. 1
B. 2
C. 3
D. None of these

Explanation

To find the order of the differential equation whose general solution is given by

\[ y = \frac{ax}{bx + c} \]

where \(a\), \(b\), and \(c\) are arbitrary constants, we can follow these steps:

### Step 1: Identify the form of the solution
The given solution can be expressed as:

\[ y = \frac{ax}{bx + c} \]

### Step 2: Determine the number of arbitrary constants
In the expression \(y = \frac{ax}{bx + c}\), we can see that there are three arbitrary constants: \(a\), \(b\), and \(c\).

### Step 3: Relate the number of arbitrary constants to the order of the differential equation
The order of a differential equation is determined by the number of arbitrary constants in its general solution. Each arbitrary constant corresponds to one order of differentiation.

### Step 4: Conclusion
Since there are three arbitrary constants (\(a\), \(b\), and \(c\)), the order of the differential equation is 3.

Thus, the order of the differential equation whose general solution is

\[ y = \frac{ax}{bx + c} \]

is **3**.

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