- #1
turpy
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Homework Statement
(x2)d2y/dx2 + 2*x*(dy/dx) + w2*x2*y=0
Where w is a constant
Homework Equations
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!