Past exam of the mathematical methods I course of the University of Oxford / 2013 / 12 / b / i / Solution

On an interval with $x\ne -1$, an integrating factor is $(x+1{)}^{-2}$. Multiplication givesIntegration therefore yieldsThe polynomial formula has a smooth continuation at $x=-1$, but the original coefficient $2/(x+1)$ is undefined there. Solution intervals for the stated equation must avoid that point, and the constants on its two sides need not agree.