Verifying a solution of a differential equation

[asilvester635]

I was contemplating why I couldn't get the derivative of y = cos(x)/x to equal to x2​y' = xy - y2 , then I realized I'm just verifying, therefore it might not be a solution. My conclusion is that y = cos(x)/x is not a solution. Do you agree with this statement?

***NOTE: I JUST NOTICED THAT I COMPLETLELY DID THIS PROBLEM WRONG. I'LL MAKE SOME CHANGES.