Concept to differential equations

[vanitymdl]

Question: Explain why you cannot solve the ordinary equation?

x^2y'' + xy' + (x^2-1)y = 0

My attempt: I don't need to solve it, but just simply state why I can't with just differential equations
So my answer is, This differential equation does have a solution, it's just not expressable in closed form.

I don't know if I should add on to this or does this get my point across

 

[LCKurtz]

Question: Explain why you cannot solve the ordinary equation?

x^2y'' + xy' + (x^2-1)y = 0

My attempt: I don't need to solve it, but just simply state why I can't with just differential equations
So my answer is, This differential equation does have a solution, it's just not expressable in closed form.

I don't know if I should add on to this or does this get my point across

Don't series solutions qualify as "just differential equations"? Is your question given in the context of studying singular points?

 

[vanitymdl]

Well this is just to refresh on my differential skills, this class is applied analysis and the professor wanted us to explain this

 

[LCKurtz]

Well, who knows what he wants. This is an example of Bessel's differential equation which has been well studied and the solutions known. See

http://mathworld.wolfram.com/BesselDifferentialEquation.html