Chapter 6.4, Problem 38E

To determine

First three positive eigenvalues and corresponding eigenfunctions of the boundary-value problem $x{y}^{″}+y^{\prime }+\lambda xy=0,y\left(x\right)\text{, }{y}^{\prime }\left(x\right)\text{ bounded as }x\to 0^{+},y\left(2\right)=0$.