Past exam of the mathematical methods I course of the University of Oxford / 2013 resit / 12 / a / Solution

Set $u=x+1$, so the equation is linear: $y^{\prime }-y/u=1+2/u$, with $u\ne 0$. An integrating factor is $1/u$ on either connected side of $u=0$. ThusConsequently the full real solution isThe original equation is undefined at $x=-1$, so a continuation of the formula through that point is not a solution on an interval containing it. Constants can be chosen independently on the two separated domain components.