# Wronskian is infinite

Given a differential equation $$xy''+y'+xy=0~.$$ I have to find the number of linearly independent solutions about $$x=0$$.

My attempt is to find the Wronskian at $$x=0$$ which is infinity. I cannot understand how to proceed.

• This is a well-studied DifEq and has solution $y(x) = c_1 J_0(x) + c_2 Y_0(x)$ in terms of Bessel Functions. You can show this, e.g., by supposing $y$ is analytic and working with the power series. Knowing this, you should get two linearly independent solutions. – Brevan Ellefsen Sep 9 '18 at 10:40
• Another thing to try (if you do not know about Bessel functions) is series solution of the DE. – GEdgar Sep 9 '18 at 10:54