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 can follow these steps:

### Step 1: Rewrite the equation
We start with the given equation:
\[ \frac{dy}{dx} = 1 \]

### Step 2: Separate variables
We can rearrange this equation to separate the variables \(dy\) and \(dx\):
\[ dy = dx \]

### Step 3: Integrate both sides
Next, we integrate both sides of the equation:
\[ \int dy = \int dx \]

### Step 4: Perform the integration
The integrals yield:
\[ y = x + C \]
where \(C\) is the constant of integration.

### Step 5: Rearranging the equation
We can express the solution in a different form:
\[ y - x = C \]

### Final Solution
Thus, the general solution of the differential equation \(\frac{dy}{dx} = 1\) is:
\[ y = x + C \]
or equivalently,
\[ y - x = C \]

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