A quastion about Diffrential equation

[Navid555]

Hello. How can i find eigenfunction, eigenvalue and orthagonality of this diffrential equation?

 

[Fermat2718]

Please share what you have attempted and where you are stuck. Let us know what background you have.

 

[nasi112]

Since \(\displaystyle \lambda \geq 0\), you should get two general solutions. Place them aside and apply the initial conditions for each one of them and see what that gives you.

If I were you, I would start with \(\displaystyle \lambda = 0\).