Given the differential equation $x \frac{dy}{dx} - y = 3$, let's solve it to understand the relationship between $x$ and $y$.

Step 1: Rearrange the Equation

We can rewrite the equation as: $x \frac{dy}{dx} = y + 3$ $\frac{dy}{dx} = \frac{y + 3}{x}$

Step 2: Solve the Differential Equation

This is a separable differential equation. We can separate the variables $y$ and $x$ as follows: $\frac{dy}{y + 3} = \frac{dx}{x}$

Step 3: Integrate Both Sides

Integrating both sides, we get: $\int \frac{dy}{y + 3} = \int \frac{dx}{x}$

The left side is a standard integral: $\ln |y + 3| = \ln |x| + C$ where $C$ is the constant of integration.

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