If the general solution of a differential equation is `y^2 + 2cy - cx + c^2 = 0`, where c is an arbitary constant, then what is the order of the differential equation ?

Options

A. 1
B. 2
C. 3
D. 4

Answer

To determine the order of the differential equation given the general solution \( y^2 + 2cy - cx + c^2 = 0 \), where \( c \) is an arbitrary constant, we can follow these steps:

### Step 1: Identify the number of arbitrary constants
The general solution of a differential equation typically includes arbitrary constants. In this case, the equation has one arbitrary constant \( c \).

### Step 2: Relate the number of arbitrary constants to the order
The order of a differential equation is defined as the highest derivative present in the equation. However, a key point is that the number of arbitrary constants in the general solution corresponds to the order of the differential equation.

### Step 3: Conclude the order of the differential equation
Since there is one arbitrary constant \( c \) in the given general solution, we conclude that the order of the differential equation is 1.

### Final Answer
The order of the differential equation is **1**.

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