The solution of `(dy)/(dx) = 1` is

Options

A. `x + y = c`
B. `xy = c`
C. `x^(2) + y^(2) = c`
D. `y - x = c`

Answer

To solve the differential equation \(\frac{dy}{dx} = 1\), we will integrate both sides with respect to \(x\).

### Step-by-step Solution:

1. **Start with the given differential equation**:
\[ \frac{dy}{dx} = 1 \]

2. **Integrate both sides**:
To find \(y\), we integrate the left side with respect to \(y\) and the right side with respect to \(x\):
\[ \int dy = \int 1 \, dx \]

3. **Perform the integration**:
The left side integrates to \(y\) and the right side integrates to \(x + C\), where \(C\) is the constant of integration:
\[ y = x + C \]

4. **Write the final solution**:
The general solution of the differential equation \(\frac{dy}{dx} = 1\) is:
\[ y = x + C \]