 Solution

Let $u_1,u_2$ be a local fundamental pair at zero, including a logarithmic Frobenius solution if the exponents are resonant. Any other independent pair on a common branch domain has $w_1=a{u}_1+b{u}_2$ and $w_2=c{u}_1+d{u}_2$ with constant coefficients and $ad-bc\ne 0$. Bilinearity and antisymmetry of the Wronskian giveThus changing the independent branches multiplies the principal-pair Wronskian by a nonzero constant, once the branches are continued onto the same domain.