Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 4 / b / ii / Solution

The integrating factor is $e^{2x}$, so the differential equation becomes $(e^{2x}y{)}^{\prime }=1$. Integration givesThe factor $x$ in the particular solution accounts for the forcing term being proportional to the homogeneous solution.