A first-order linear differential equation can be expressed in the form:

`dy/dx + P(x)y = Q(x)`

where P(x) and Q(x) are functions of x, and y is the dependent variable.

To solve a first-order linear differential equation, follow these steps:

1. **Identify P(x) and Q(x):** In the given differential equation, identify the functions P(x) and Q(x) which are multiplying the dependent variable y and existing on the right-hand side of the equation, respectively.

2. **Find the integrating factor (IF):** Calculate the integrating factor, which is the exponential of the integral of P(x) with respect to x. The integrating factor can be found using this formula:

   `IF = e^(∫P(x)dx)`

3. **Multiply the entire equation by the integrating factor:** To eliminate the y term from the left-hand side, multiply both sides of the differential equation by the integrating factor:

   `IF(dy/dx) + IF(P(x)y) = IF(Q(x))`

4. **Integrate both sides of the equation:** Now, the left-hand side of the equation is an exact differential, so you can integrate both sides with respect to x:

   `∫(IF(dy/dx) + IF(P(x)y))dx = ∫(IF(Q(x)))dx`

   Since the left-hand side is an exact differential, it simplifies to:

   `∫(d(IF*y)) = ∫(IF(Q(x)))dx`

5. **Solve for y:** Integrate both sides of the equation, and then divide both sides by the integrating factor to isolate y:

   `y = (1/IF) * ∫(IF(Q(x)))dx + C/IF`

   where C is the constant of integration. The function y(x) is now the general solution to the given first-order linear differential equation.

**Note:** If you have an initial condition, say y(x0) = y0, you can use it to find the value of the constant of integration C, and obtain the particular solution for the differential equation.
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