Question

How do i find a simplified expression for
W=e^(-∫p(x)dx) of (x-1)y''-xy'+y=0, x>1 given y1=x ??????? I did y''-(x/x-1)y'+(1/x-1)y=0 but dont know how to find a simplified expression help :)

Answer 1

\[\large{y''+\frac{x}{x-1}y'+\frac{1}{x-1}y=0}\]\[\huge{W=e^{-\int\limits{\frac{x}{x-1}dx}}}\]\[\huge{W=e^{-(x+\ln(x-1))}}\]\[\huge{W=e^{-x-\ln(x-1)}=e^{-x}e^{-\ln(x-1)}}\]\[\large{=\frac{1}{e^x(x-1)}}\]