## Step-by-step Solution

Problem to solve:

Learn how to solve differential equations problems step by step online.

$\frac{dy}{dx}-1\cdot -2y=x+12$

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=x-2y+12. Rearrange the differential equation. Simplifying. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(x)=2 and Q(x)=x+12. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(x), we first need to calculate \int P(x)dx.