Series Solutions · Superchallenge problem

Let $u$ and $v$ be the power-series solutions of $y'' + 2x\,y' + 5y = 0$ with $u(0) = 1$, $u'(0) = 0$ and $v(0) = 0$, $v'(0) = 1$. Find the exact value of $u(1)\,v'(1) - u'(1)\,v(1)$.