## anonymous 4 years ago "Consider equation x^2y''-2xy'+2y=0, x>0 What differential equation does the Wronskian W(x)=W[y1,y2](x) for any pair of solutions of the above equation satisfy?"

Abel's theorem states that if $$y_1(x)$$ and $$y_2(x)$$ are two solutions to$y''+p(x)y'+q(x)y=0,$then the Wronskian of the two solutions is$W(y_1,y_2)(x)=c\exp\left[-\int p(x)\,dx\right].$For this case, we have that $$p(x)=-2/x$$. Hence$W(y_1,y_2)(x)=cx^2.$