1. The problem statement, all variables and given/known data (x2)d2y/dx2 + 2*x*(dy/dx) + w2*x2*y=0 Where w is a constant 2. Relevant equations 3. The attempt at a solution I am having a really hard time figuring out how to solve this. Usually for second order linear ODEs I start with assuming a solution of form y=eλx, substitute into the equation, find the two roots and get the solution as y= c1*y1+ c2*y2. It doesn't work in this case though. From another solver I found that the solution has the form of C1*sin(wx)/x + C2*cos(wx)/x. With sin and cos present, usually the method I mentioned above has to yield complex conjugate roots. But I'm really puzzled by the x's in the denominators. What kind of solution form would I have to assume to get that? Any help would be appreciated, thanks!