Find $W(y_1 , y_2)$ where $y_1$ and $y_2$ are fundamental solutions of $x^2 y'' - 2 x^3 y' + \frac{1}{x^2} y = 0$

Question

Find $W(y_1 , y_2)$ where $y_1$ and $y_2$ are fundamental solutions of $x^2 y'' - 2 x^3 y' + \frac{1}{x^2} y = 0$

I tried to find solutions on Wolfram yet haven't got any solutions but just stated "Sturm-Liouville". How do you find the Wronskian of the solutions of this D.E.?

Answer 1

$$x^2 y'' - 2 x^3 y' + \frac{1}{x^2} y = 0$$ $$y'' - 2 x y' + \frac{1}{x^4} y = 0$$ For the second order differential equation: $$y''+p(x)y'+q(x)y=0$$ You can use Abel's identity $$W'=-p(x)W$$ $$\ln W=-\int p(x)dx$$