Original equation: xy'' + y' + 0. I have found that the roots are both 0, and one of the solutions is:

$\displaystyle y_1=\sum_{m=0}^\infty \frac{(-1)^m a_0}{(m!)^2}x^m$

That solution checks. For y2, I tried using $\displaystyle y_2 = y_1 \int \frac{e^{-\int P(x) dx}}{{y_1}^2}dx$, but using P(x) = 1/x, y2 turned into:

$\displaystyle y_2 = y_1(ln(x) + \frac{x}{2} + \frac{19x^2}{288} + \frac{7x^3}{864} + ...)$

which is not even close to the answer in the back of the book. Please advise.