How to Solve Sturm-Liouville Problems to Find Eigen Value and Eigenfunction?

[HansLee]

I have a problem about Sturm-Liouville, and i can't solve it, maybe someone can help me

x² y''+ 2xy'+ λy=0

and y(0)=0, y(e²)=0

What is the eigen value and eigenfunction of the equation?

 

[Astronuc]

Has one tried y=xⁿ?

 

[HansLee]

Ooo thanks, actually I have tried y=xⁿ before, but there's a miscalculate. But when I see ur suggestion, I tried once again and got the answer. Thanks