1. The problem statement, all variables and given/known data Find a second solution y2 for x^2*y"+xy'-y=0; y1=x that isn't a constant multiple of the solution y1. 2. Relevant equations None. 3. The attempt at a solution Here's my work: I divided by x^2, y"+(1/x)y'-(1/x^2)y=0 P(x)=1/x and Q(x)=-1/x^2 Let y(x)=v(x)*x y'(x)=v'(x)*x+v(x) (1/x)y'(x)=v'(x)+v(x)/x y"(x)=v'(x)+v"(x)*x+v'(x)=xv"(x)+2v'(x) xv"(x)+2v'(x)+v'(x)+v(x)/x-v(x)*x/(x^2)=0 xv"(x)+3v'(x)=0 Let w=v' w'=v" xw'+3w=0 w'=-3w/x dw/dx=-3w/x dw/w=-3/x dx integrate ln abs(w)=-3ln abs(x)+C Don't count C, the constant. w=1/x^3 w=v'=1/x^3 dv/dx=1/x^2 don't count c, the constant. v=-1/2x^2 y=v*x y=-1/2x^2*x=-1/2x But the answer in the book is y2=1/x. I got y=-1/2x, which answer is right?