related to eigen value eigen function

Question

$\frac{d}{dx}(x\frac{dy}{dx}+\frac{λ}{x}y)=0$ where $λ>0$

Find the eigen value and eigen function using the condtion $y(0)+y_1(0)=0$ and $y(1)+y_1(1)=0$

May be it is easy, I try this but did not understand how to solve this?

Answer 1

Your D.E. will be $$\frac{dy}{dx}+\frac{\lambda}{x^2}y=\frac{c}{x}$$, c is constant. Solve this 1st order linear D.E. using Integrating Factor method and try to find the condition so that the D.E. doesn't have a trivial solution.