Ok, I think I know what to do now, lol. I was on the right track... Just define $\displaystyle P(x)=\frac{a_1(x)}{a_2(x)}$ and $\displaystyle Q(x)=\frac{a_o(x)}{a_2(x)}$, basically divide the first two equations (from my failed system) by the coefficient of y'' to get:

$\displaystyle y_1''+P(x)y'_1+Q(x)y_1=0$

$\displaystyle y_2''+P(x)y'_2+Q(x)y_2=0$

From the first:

$\displaystyle P(x)=-Q(x)x$

Now substitute into the second:

$\displaystyle 2-Q(x)2x^2+Q(x)x^2=0$

$\displaystyle Q(x)=\frac{2}{x^2}$

That should help...

Remember we defined $\displaystyle Q(x)=\frac{a_o(x)}{a_2(x)}$.