Find the basic solutions at x_{0} = 1<br />
x^2\varphi''+x\varphi'+\lambda\varphi=0

x^m\left[m(m-1)+m+\lambda\right]=0\Rightarrow x^m\left[m^2+\lambda\right]=0

m=\pm i\sqrt{\lambda}

\varphi(x)=C_1\cos\left(\sqrt{\lambda}\ln(x)\right  )+C_2\sin\left(\sqrt{\lambda}\ln(x)\right)

How do I find the basic solutions around x_{0} = 1\text{?}