It is one of the most simple linear ordinary differential equation of the first order. I am sure that the method to solve it is explained in your textbook.
The first step consists in solving the homogeneous equation (A*x+B)*y'(x) + y(x) =0 (separate the variables)
The second step is to find a particular solution of the whole equation (A*x+B)*y'(x) + y(x) =1 (obvious)
The third step is to add the results of the two preceeding steps in order to obtain the general solution.
Sorry, it is not of use to detail on the forum what one can find in any texbook on differential equations.
Good work !