= Solution
The defining <Wronskian> identity gives the <first-order linear differential equation>
$$
\boxed{y_2'-\frac{y_1'}{y_1}y_2=\frac{W}{y_1}.}
$$
Work first on an interval where $y_1\ne0$. Dividing by $y_1$ recognizes a <derivative>:
$$
\left(\frac{y_2}{y_1}\right)'=\frac{W}{y_1^2},\qquad \boxed{y_2(x)=y_1(x)\left(C+\int_{x_0}^x\frac{W(s)}{y_1(s)^2}\,ds\right).}
$$
This is <reduction of order>. Choose the nonzero <Wronskian> from the <Abel identity> to obtain <linear independence>. The constant $C$ only adds a multiple of $y_1$. If $y_1$ has zeros, this quotient formula is local; the resulting solution can be continued across ordinary zeros using the original <second-order linear differential equation>.
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