Solve : `dy= sin x dx`.

Answer

To solve the differential equation given by \( dy = \sin x \, dx \), we will follow these steps:

### Step 1: Separate the variables
The equation is already in a separable form:
\[ dy = \sin x \, dx \]

### Step 2: Integrate both sides
We will integrate both sides of the equation:
\[ \int dy = \int \sin x \, dx \]

### Step 3: Perform the integration
The left side integrates to:
\[ y = \int dy = y \]
The right side integrates to:
\[ \int \sin x \, dx = -\cos x + C \]
where \( C \) is the constant of integration.

### Step 4: Combine the results
Putting it all together, we have:
\[ y = -\cos x + C \]

### Final Solution
Thus, the solution to the differential equation \( dy = \sin x \, dx \) is:
\[ y = -\cos x + C \]

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